Properties

Label 45.5
Level 45
Weight 5
Dimension 194
Nonzero newspaces 6
Newform subspaces 10
Sturm bound 720
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 10 \)
Sturm bound: \(720\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(45))\).

Total New Old
Modular forms 320 222 98
Cusp forms 256 194 62
Eisenstein series 64 28 36

Trace form

\( 194 q - 2 q^{3} - 26 q^{4} + 48 q^{5} + 182 q^{6} + 32 q^{7} - 192 q^{8} - 346 q^{9} + 14 q^{10} - 366 q^{11} - 28 q^{12} + 1134 q^{13} + 2280 q^{14} + 670 q^{15} - 1022 q^{16} - 1806 q^{17} - 4160 q^{18}+ \cdots + 98080 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(45))\)

We only show spaces with odd 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
45.5.c \(\chi_{45}(26, \cdot)\) 45.5.c.a 4 1
45.5.d \(\chi_{45}(44, \cdot)\) 45.5.d.a 8 1
45.5.g \(\chi_{45}(28, \cdot)\) 45.5.g.a 2 2
45.5.g.b 2
45.5.g.c 2
45.5.g.d 4
45.5.g.e 8
45.5.h \(\chi_{45}(14, \cdot)\) 45.5.h.a 44 2
45.5.i \(\chi_{45}(11, \cdot)\) 45.5.i.a 32 2
45.5.k \(\chi_{45}(7, \cdot)\) 45.5.k.a 88 4

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

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