Properties

Label 45.2
Level 45
Weight 2
Dimension 39
Nonzero newspaces 6
Newform subspaces 7
Sturm bound 288
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 7 \)
Sturm bound: \(288\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(45))\).

Total New Old
Modular forms 104 65 39
Cusp forms 41 39 2
Eisenstein series 63 26 37

Trace form

\( 39 q - 7 q^{2} - 8 q^{3} - 11 q^{4} - 9 q^{5} - 16 q^{6} - 12 q^{7} - 3 q^{8} - 4 q^{9} - 15 q^{10} - 4 q^{11} + 8 q^{12} - 2 q^{13} + 12 q^{14} + 4 q^{15} - 7 q^{16} + 2 q^{17} + 16 q^{18} - 20 q^{19}+ \cdots - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)

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
45.2.a \(\chi_{45}(1, \cdot)\) 45.2.a.a 1 1
45.2.b \(\chi_{45}(19, \cdot)\) 45.2.b.a 2 1
45.2.e \(\chi_{45}(16, \cdot)\) 45.2.e.a 2 2
45.2.e.b 6
45.2.f \(\chi_{45}(8, \cdot)\) 45.2.f.a 4 2
45.2.j \(\chi_{45}(4, \cdot)\) 45.2.j.a 8 2
45.2.l \(\chi_{45}(2, \cdot)\) 45.2.l.a 16 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

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