Properties

Label 45.8
Level 45
Weight 8
Dimension 351
Nonzero newspaces 6
Newform subspaces 19
Sturm bound 1152
Trace bound 1

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Defining parameters

Level: \( N \) = \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 19 \)
Sturm bound: \(1152\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(45))\).

Total New Old
Modular forms 536 377 159
Cusp forms 472 351 121
Eisenstein series 64 26 38

Trace form

\( 351 q + 32 q^{2} - 56 q^{3} + 82 q^{4} + 591 q^{5} + 2450 q^{6} - 2492 q^{7} - 11184 q^{8} - 6304 q^{9} + 8798 q^{10} + 29708 q^{11} - 2800 q^{12} - 26222 q^{13} - 16452 q^{14} - 24008 q^{15} - 16758 q^{16}+ \cdots + 47668372 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(45))\)

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

Label \(\chi\) Newforms Dimension \(\chi\) degree
45.8.a \(\chi_{45}(1, \cdot)\) 45.8.a.a 1 1
45.8.a.b 1
45.8.a.c 1
45.8.a.d 1
45.8.a.e 1
45.8.a.f 1
45.8.a.g 1
45.8.a.h 2
45.8.a.i 2
45.8.b \(\chi_{45}(19, \cdot)\) 45.8.b.a 2 1
45.8.b.b 2
45.8.b.c 4
45.8.b.d 8
45.8.e \(\chi_{45}(16, \cdot)\) 45.8.e.a 26 2
45.8.e.b 30
45.8.f \(\chi_{45}(8, \cdot)\) 45.8.f.a 4 2
45.8.f.b 24
45.8.j \(\chi_{45}(4, \cdot)\) 45.8.j.a 80 2
45.8.l \(\chi_{45}(2, \cdot)\) 45.8.l.a 160 4

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(45)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 1}\)