Properties

Label 5290.2
Level 5290
Weight 2
Dimension 255067
Nonzero newspaces 12
Sturm bound 3351744

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Defining parameters

Level: \( N \) = \( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(3351744\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5290))\).

Total New Old
Modular forms 843920 255067 588853
Cusp forms 831953 255067 576886
Eisenstein series 11967 0 11967

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5290))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
5290.2.a \(\chi_{5290}(1, \cdot)\) 5290.2.a.a 1 1
5290.2.a.b 1
5290.2.a.c 1
5290.2.a.d 1
5290.2.a.e 2
5290.2.a.f 2
5290.2.a.g 2
5290.2.a.h 2
5290.2.a.i 2
5290.2.a.j 2
5290.2.a.k 2
5290.2.a.l 2
5290.2.a.m 2
5290.2.a.n 2
5290.2.a.o 2
5290.2.a.p 3
5290.2.a.q 3
5290.2.a.r 3
5290.2.a.s 4
5290.2.a.t 4
5290.2.a.u 4
5290.2.a.v 4
5290.2.a.w 4
5290.2.a.x 4
5290.2.a.y 4
5290.2.a.z 4
5290.2.a.ba 4
5290.2.a.bb 4
5290.2.a.bc 5
5290.2.a.bd 5
5290.2.a.be 6
5290.2.a.bf 6
5290.2.a.bg 10
5290.2.a.bh 10
5290.2.a.bi 10
5290.2.a.bj 10
5290.2.a.bk 15
5290.2.a.bl 15
5290.2.b \(\chi_{5290}(1059, \cdot)\) n/a 252 1
5290.2.e \(\chi_{5290}(1057, \cdot)\) n/a 504 2
5290.2.g \(\chi_{5290}(501, \cdot)\) n/a 1680 10
5290.2.j \(\chi_{5290}(399, \cdot)\) n/a 2520 10
5290.2.k \(\chi_{5290}(231, \cdot)\) n/a 4048 22
5290.2.m \(\chi_{5290}(63, \cdot)\) n/a 5040 20
5290.2.p \(\chi_{5290}(139, \cdot)\) n/a 6072 22
5290.2.r \(\chi_{5290}(137, \cdot)\) n/a 12144 44
5290.2.s \(\chi_{5290}(31, \cdot)\) n/a 40480 220
5290.2.t \(\chi_{5290}(9, \cdot)\) n/a 60720 220
5290.2.w \(\chi_{5290}(7, \cdot)\) n/a 121440 440

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5290))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5290)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1058))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2645))\)\(^{\oplus 2}\)