Properties

Label 90.5
Level 90
Weight 5
Dimension 212
Nonzero newspaces 6
Newform subspaces 13
Sturm bound 2160
Trace bound 4

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Defining parameters

Level: \( N \) = \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 13 \)
Sturm bound: \(2160\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(90))\).

Total New Old
Modular forms 928 212 716
Cusp forms 800 212 588
Eisenstein series 128 0 128

Trace form

\( 212 q - 12 q^{3} - 64 q^{4} - 78 q^{5} - 96 q^{6} + 72 q^{7} + 436 q^{9} - 96 q^{10} + 360 q^{11} - 32 q^{12} - 880 q^{13} - 576 q^{14} - 438 q^{15} + 256 q^{16} + 2580 q^{17} + 2048 q^{18} + 1880 q^{19}+ \cdots - 89084 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(90))\)

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
90.5.b \(\chi_{90}(89, \cdot)\) 90.5.b.a 8 1
90.5.d \(\chi_{90}(71, \cdot)\) 90.5.d.a 4 1
90.5.d.b 4
90.5.g \(\chi_{90}(37, \cdot)\) 90.5.g.a 2 2
90.5.g.b 2
90.5.g.c 4
90.5.g.d 4
90.5.g.e 4
90.5.g.f 4
90.5.h \(\chi_{90}(11, \cdot)\) 90.5.h.a 32 2
90.5.j \(\chi_{90}(29, \cdot)\) 90.5.j.a 48 2
90.5.k \(\chi_{90}(7, \cdot)\) 90.5.k.a 48 4
90.5.k.b 48

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(90))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(90)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)