# Properties

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

## 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 available 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

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