## Defining parameters

 Level: $$N$$ = $$5625 = 3^{2} \cdot 5^{4}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$4500000$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5625))$$.

Total New Old
Modular forms 1133800 824256 309544
Cusp forms 1116201 817344 298857
Eisenstein series 17599 6912 10687

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5625))$$

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
5625.2.a $$\chi_{5625}(1, \cdot)$$ 5625.2.a.a 2 1
5625.2.a.b 2
5625.2.a.c 2
5625.2.a.d 2
5625.2.a.e 2
5625.2.a.f 2
5625.2.a.g 2
5625.2.a.h 2
5625.2.a.i 4
5625.2.a.j 4
5625.2.a.k 4
5625.2.a.l 4
5625.2.a.m 4
5625.2.a.n 4
5625.2.a.o 6
5625.2.a.p 6
5625.2.a.q 6
5625.2.a.r 6
5625.2.a.s 8
5625.2.a.t 8
5625.2.a.u 8
5625.2.a.v 8
5625.2.a.w 8
5625.2.a.x 8
5625.2.a.y 8
5625.2.a.z 8
5625.2.a.ba 8
5625.2.a.bb 8
5625.2.a.bc 8
5625.2.a.bd 8
5625.2.a.be 8
5625.2.a.bf 24
5625.2.b $$\chi_{5625}(3124, \cdot)$$ n/a 192 1
5625.2.e $$\chi_{5625}(1876, \cdot)$$ n/a 928 2
5625.2.f $$\chi_{5625}(3932, \cdot)$$ n/a 320 2
5625.2.h $$\chi_{5625}(1126, \cdot)$$ n/a 776 4
5625.2.k $$\chi_{5625}(1249, \cdot)$$ n/a 928 2
5625.2.m $$\chi_{5625}(874, \cdot)$$ n/a 776 4
5625.2.p $$\chi_{5625}(182, \cdot)$$ n/a 1856 4
5625.2.q $$\chi_{5625}(376, \cdot)$$ n/a 3744 8
5625.2.s $$\chi_{5625}(557, \cdot)$$ n/a 1280 8
5625.2.t $$\chi_{5625}(226, \cdot)$$ n/a 3700 20
5625.2.v $$\chi_{5625}(124, \cdot)$$ n/a 3744 8
5625.2.y $$\chi_{5625}(199, \cdot)$$ n/a 3680 20
5625.2.ba $$\chi_{5625}(68, \cdot)$$ n/a 7488 16
5625.2.bc $$\chi_{5625}(76, \cdot)$$ n/a 17760 40
5625.2.be $$\chi_{5625}(107, \cdot)$$ n/a 6000 40
5625.2.bf $$\chi_{5625}(46, \cdot)$$ n/a 31100 100
5625.2.bg $$\chi_{5625}(49, \cdot)$$ n/a 17760 40
5625.2.bl $$\chi_{5625}(19, \cdot)$$ n/a 31200 100
5625.2.bn $$\chi_{5625}(32, \cdot)$$ n/a 35520 80
5625.2.bo $$\chi_{5625}(16, \cdot)$$ n/a 149600 200
5625.2.bq $$\chi_{5625}(8, \cdot)$$ n/a 50000 200
5625.2.br $$\chi_{5625}(4, \cdot)$$ n/a 149600 200
5625.2.bv $$\chi_{5625}(2, \cdot)$$ n/a 299200 400

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5625))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5625)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(125))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(375))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(625))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1125))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1875))$$$$^{\oplus 2}$$