Properties

Label 45.4
Level 45
Weight 4
Dimension 143
Nonzero newspaces 6
Newform subspaces 13
Sturm bound 576
Trace bound 1

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Defining parameters

Level: \( N \) = \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 13 \)
Sturm bound: \(576\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(45))\).

Total New Old
Modular forms 248 169 79
Cusp forms 184 143 41
Eisenstein series 64 26 38

Trace form

\( 143 q - 2 q^{2} - 2 q^{3} + 30 q^{4} + 6 q^{5} - 34 q^{6} - 24 q^{7} - 72 q^{8} - 34 q^{9} + 88 q^{10} + 124 q^{11} + 176 q^{12} - 116 q^{13} - 348 q^{14} - 203 q^{15} - 598 q^{16} - 566 q^{17} - 440 q^{18}+ \cdots - 134 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)

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
45.4.a \(\chi_{45}(1, \cdot)\) 45.4.a.a 1 1
45.4.a.b 1
45.4.a.c 1
45.4.a.d 1
45.4.a.e 1
45.4.b \(\chi_{45}(19, \cdot)\) 45.4.b.a 2 1
45.4.b.b 4
45.4.e \(\chi_{45}(16, \cdot)\) 45.4.e.a 4 2
45.4.e.b 6
45.4.e.c 14
45.4.f \(\chi_{45}(8, \cdot)\) 45.4.f.a 12 2
45.4.j \(\chi_{45}(4, \cdot)\) 45.4.j.a 32 2
45.4.l \(\chi_{45}(2, \cdot)\) 45.4.l.a 64 4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

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