G = Gamma0(11); G
Congruence Subgroup Gamma0(11) Congruence Subgroup Gamma0(11) |
# I haven't finished implementing a G.generators() command..., but you probably # don't care.
G.coset_reps()
<generator object at 0xad893aec> <generator object at 0xad893aec> |
list(G.coset_reps())
[[1, 0, 0, 1], [0, -1, 1, 0], [0, -1, 1, 1], [0, -1, 1, 2], [0, -1, 1, 3], [0, -1, 1, 4], [0, -1, 1, 5], [0, -1, 1, 6], [0, -1, 1, 7], [0, -1, 1, 8], [0, -1, 1, 9], [0, -1, 1, 10]] [[1, 0, 0, 1], [0, -1, 1, 0], [0, -1, 1, 1], [0, -1, 1, 2], [0, -1, 1, 3], [0, -1, 1, 4], [0, -1, 1, 5], [0, -1, 1, 6], [0, -1, 1, 7], [0, -1, 1, 8], [0, -1, 1, 9], [0, -1, 1, 10]] |
dimension_cusp_forms(11,2)
1 1 |
dimension_cusp_forms(Gamma1(13),2)
2 2 |
dimension_cusp_forms(100,2)
7 7 |
dimension_new_cusp_forms(Gamma1(100),2)
141 141 |
G.<a,b> = DirichletGroup(4*37) G
Group of Dirichlet characters of modulus 148 over Cyclotomic Field of order 36 and degree 12 Group of Dirichlet characters of modulus 148 over Cyclotomic Field of order 36 and degree 12 |
G.unit_gens()
[75, 113] [75, 113] |
# Printing a character gives the values of the character on the # generators 75 and 113 for (Z/NZ)^* print "a = ", a print "b = ", b
a = [-1, 1] b = [1, zeta36] a = [-1, 1] b = [1, zeta36] |
order(b)
36 36 |
[b(n) for n in range(1,11)]
[1, 0, -zeta36^8, 0, -zeta36^5, 0, -zeta36^8 + zeta36^2, 0, zeta36^10 - zeta36^4, 0] [1, 0, -zeta36^8, 0, -zeta36^5, 0, -zeta36^8 + zeta36^2, 0, zeta36^10 - zeta36^4, 0] |
b.element()
(0, 1) (0, 1) |
b.values_on_gens()
(1, zeta36) (1, zeta36) |
G([-1,-1])
[-1, -1] [-1, -1] |
dimension_cusp_forms(a,3)
36 36 |
dimension_cusp_forms(b,3)
35 35 |