Properties

Label 90.18
Level 90
Weight 18
Dimension 885
Nonzero newspaces 6
Sturm bound 7776
Trace bound 1

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Defining parameters

Level: \( N \) = \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(7776\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(90))\).

Total New Old
Modular forms 3736 885 2851
Cusp forms 3608 885 2723
Eisenstein series 128 0 128

Trace form

\( 885 q + 768 q^{2} - 954 q^{3} + 1245184 q^{4} + 997457 q^{5} - 14550528 q^{6} + 21245772 q^{7} - 50331648 q^{8} + 1134224890 q^{9} - 1026886400 q^{10} + 3212251078 q^{11} + 597164032 q^{12} + 227537786 q^{13}+ \cdots - 21\!\cdots\!68 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(90))\)

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
90.18.a \(\chi_{90}(1, \cdot)\) 90.18.a.a 1 1
90.18.a.b 1
90.18.a.c 1
90.18.a.d 1
90.18.a.e 1
90.18.a.f 1
90.18.a.g 1
90.18.a.h 2
90.18.a.i 2
90.18.a.j 2
90.18.a.k 2
90.18.a.l 2
90.18.a.m 2
90.18.a.n 2
90.18.a.o 3
90.18.a.p 3
90.18.c \(\chi_{90}(19, \cdot)\) 90.18.c.a 8 1
90.18.c.b 8
90.18.c.c 10
90.18.c.d 16
90.18.e \(\chi_{90}(31, \cdot)\) n/a 136 2
90.18.f \(\chi_{90}(17, \cdot)\) 90.18.f.a 32 2
90.18.f.b 36
90.18.i \(\chi_{90}(49, \cdot)\) n/a 204 2
90.18.l \(\chi_{90}(23, \cdot)\) n/a 408 4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(90))\) into lower level spaces

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