Properties

Label 90.3
Level 90
Weight 3
Dimension 102
Nonzero newspaces 5
Newform subspaces 10
Sturm bound 1296
Trace bound 1

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Defining parameters

Level: \( N \) = \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 10 \)
Sturm bound: \(1296\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(90))\).

Total New Old
Modular forms 496 102 394
Cusp forms 368 102 266
Eisenstein series 128 0 128

Trace form

\( 102 q - 2 q^{2} + 18 q^{5} + 24 q^{6} + 16 q^{7} + 4 q^{8} + 16 q^{9} + 42 q^{10} + 44 q^{11} - 8 q^{12} + 26 q^{13} - 72 q^{14} - 42 q^{15} - 8 q^{16} - 130 q^{17} - 16 q^{18} - 16 q^{19} - 40 q^{20} + 36 q^{21}+ \cdots + 868 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(90))\)

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
90.3.b \(\chi_{90}(89, \cdot)\) 90.3.b.a 4 1
90.3.d \(\chi_{90}(71, \cdot)\) None 0 1
90.3.g \(\chi_{90}(37, \cdot)\) 90.3.g.a 2 2
90.3.g.b 2
90.3.g.c 2
90.3.g.d 4
90.3.h \(\chi_{90}(11, \cdot)\) 90.3.h.a 16 2
90.3.j \(\chi_{90}(29, \cdot)\) 90.3.j.a 8 2
90.3.j.b 16
90.3.k \(\chi_{90}(7, \cdot)\) 90.3.k.a 24 4
90.3.k.b 24

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(90))\) into lower level spaces

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