Properties

Label 45.6
Level 45
Weight 6
Dimension 249
Nonzero newspaces 6
Newform subspaces 15
Sturm bound 864
Trace bound 1

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Defining parameters

Level: N N = 45=325 45 = 3^{2} \cdot 5
Weight: k k = 6 6
Nonzero newspaces: 6 6
Newform subspaces: 15 15
Sturm bound: 864864
Trace bound: 11

Dimensions

The following table gives the dimensions of various subspaces of M6(Γ1(45))M_{6}(\Gamma_1(45)).

Total New Old
Modular forms 392 275 117
Cusp forms 328 249 79
Eisenstein series 64 26 38

Trace form

249q20q2+16q3+34q4141q5358q6+212q7+1968q8+944q92414q103188q115200q12+1466q13+5148q14+4216q15+3530q16+6658q17++1056748q99+O(q100) 249 q - 20 q^{2} + 16 q^{3} + 34 q^{4} - 141 q^{5} - 358 q^{6} + 212 q^{7} + 1968 q^{8} + 944 q^{9} - 2414 q^{10} - 3188 q^{11} - 5200 q^{12} + 1466 q^{13} + 5148 q^{14} + 4216 q^{15} + 3530 q^{16} + 6658 q^{17}+ \cdots + 1056748 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S6new(Γ1(45))S_{6}^{\mathrm{new}}(\Gamma_1(45))

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space Sknew(N,χ) S_k^{\mathrm{new}}(N, \chi) we list available newforms together with their dimension.

Label χ\chi Newforms Dimension χ\chi degree
45.6.a χ45(1,)\chi_{45}(1, \cdot) 45.6.a.a 1 1
45.6.a.b 1
45.6.a.c 1
45.6.a.d 2
45.6.a.e 2
45.6.a.f 2
45.6.b χ45(19,)\chi_{45}(19, \cdot) 45.6.b.a 2 1
45.6.b.b 2
45.6.b.c 4
45.6.b.d 4
45.6.e χ45(16,)\chi_{45}(16, \cdot) 45.6.e.a 18 2
45.6.e.b 22
45.6.f χ45(8,)\chi_{45}(8, \cdot) 45.6.f.a 20 2
45.6.j χ45(4,)\chi_{45}(4, \cdot) 45.6.j.a 56 2
45.6.l χ45(2,)\chi_{45}(2, \cdot) 45.6.l.a 112 4

Decomposition of S6old(Γ1(45))S_{6}^{\mathrm{old}}(\Gamma_1(45)) into lower level spaces

S6old(Γ1(45)) S_{6}^{\mathrm{old}}(\Gamma_1(45)) \cong S6new(Γ1(1))S_{6}^{\mathrm{new}}(\Gamma_1(1))6^{\oplus 6}\oplusS6new(Γ1(3))S_{6}^{\mathrm{new}}(\Gamma_1(3))4^{\oplus 4}\oplusS6new(Γ1(5))S_{6}^{\mathrm{new}}(\Gamma_1(5))3^{\oplus 3}\oplusS6new(Γ1(9))S_{6}^{\mathrm{new}}(\Gamma_1(9))2^{\oplus 2}\oplusS6new(Γ1(15))S_{6}^{\mathrm{new}}(\Gamma_1(15))2^{\oplus 2}