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Properties

Label 45.10
Level 45
Weight 10
Dimension 457
Nonzero newspaces 6
Newform subspaces 17
Sturm bound 1440
Trace bound 1

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Defining parameters

Level: N N = 45=32⋅5 45 = 3^{2} \cdot 5
Weight: k k = 10 10
Nonzero newspaces: 6 6
Newform subspaces: 17 17
Sturm bound: 14401440
Trace bound: 11

Dimensions

The following table gives the dimensions of various subspaces of M10(Γ1(45))M_{10}(\Gamma_1(45)).

Total New Old
Modular forms 680 483 197
Cusp forms 616 457 159
Eisenstein series 64 26 38

Trace form

457q−88q2−2q3+2642q4−1536q5−4894q6+22488q7−24336q8−8926q9+113846q10−188644q11+179312q12+82664q13+192012q14−482099q15+⋯−4109380118q99+O(q100) 457 q - 88 q^{2} - 2 q^{3} + 2642 q^{4} - 1536 q^{5} - 4894 q^{6} + 22488 q^{7} - 24336 q^{8} - 8926 q^{9} + 113846 q^{10} - 188644 q^{11} + 179312 q^{12} + 82664 q^{13} + 192012 q^{14} - 482099 q^{15}+ \cdots - 4109380118 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S10new(Γ1(45))S_{10}^{\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
45.10.a χ45(1,⋅)\chi_{45}(1, \cdot) 45.10.a.a 1 1
45.10.a.b 1
45.10.a.c 1
45.10.a.d 2
45.10.a.e 2
45.10.a.f 2
45.10.a.g 3
45.10.a.h 3
45.10.b χ45(19,⋅)\chi_{45}(19, \cdot) 45.10.b.a 2 1
45.10.b.b 4
45.10.b.c 8
45.10.b.d 8
45.10.e χ45(16,⋅)\chi_{45}(16, \cdot) 45.10.e.a 34 2
45.10.e.b 38
45.10.f χ45(8,⋅)\chi_{45}(8, \cdot) 45.10.f.a 36 2
45.10.j χ45(4,⋅)\chi_{45}(4, \cdot) 45.10.j.a 104 2
45.10.l χ45(2,⋅)\chi_{45}(2, \cdot) 45.10.l.a 208 4

Decomposition of S10old(Γ1(45))S_{10}^{\mathrm{old}}(\Gamma_1(45)) into lower level spaces

S10old(Γ1(45))≅ S_{10}^{\mathrm{old}}(\Gamma_1(45)) \cong S10new(Γ1(1))S_{10}^{\mathrm{new}}(\Gamma_1(1))⊕6^{\oplus 6}⊕\oplusS10new(Γ1(3))S_{10}^{\mathrm{new}}(\Gamma_1(3))⊕4^{\oplus 4}⊕\oplusS10new(Γ1(5))S_{10}^{\mathrm{new}}(\Gamma_1(5))⊕3^{\oplus 3}⊕\oplusS10new(Γ1(9))S_{10}^{\mathrm{new}}(\Gamma_1(9))⊕2^{\oplus 2}⊕\oplusS10new(Γ1(15))S_{10}^{\mathrm{new}}(\Gamma_1(15))⊕2^{\oplus 2}