## Defining parameters

 Level: $$N$$ = $$5780 = 2^{2} \cdot 5 \cdot 17^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$3995136$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5780))$$.

Total New Old
Modular forms 1006784 532595 474189
Cusp forms 990785 528171 462614
Eisenstein series 15999 4424 11575

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5780))$$

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
5780.2.a $$\chi_{5780}(1, \cdot)$$ 5780.2.a.a 1 1
5780.2.a.b 1
5780.2.a.c 1
5780.2.a.d 1
5780.2.a.e 1
5780.2.a.f 1
5780.2.a.g 2
5780.2.a.h 2
5780.2.a.i 3
5780.2.a.j 3
5780.2.a.k 3
5780.2.a.l 6
5780.2.a.m 6
5780.2.a.n 6
5780.2.a.o 6
5780.2.a.p 12
5780.2.a.q 12
5780.2.a.r 12
5780.2.a.s 12
5780.2.c $$\chi_{5780}(5201, \cdot)$$ 5780.2.c.a 2 1
5780.2.c.b 2
5780.2.c.c 2
5780.2.c.d 2
5780.2.c.e 4
5780.2.c.f 6
5780.2.c.g 12
5780.2.c.h 12
5780.2.c.i 24
5780.2.c.j 24
5780.2.e $$\chi_{5780}(3469, \cdot)$$ n/a 136 1
5780.2.g $$\chi_{5780}(2889, \cdot)$$ n/a 136 1
5780.2.i $$\chi_{5780}(1407, \cdot)$$ n/a 1564 2
5780.2.l $$\chi_{5780}(4047, \cdot)$$ n/a 1566 2
5780.2.m $$\chi_{5780}(829, \cdot)$$ n/a 272 2
5780.2.o $$\chi_{5780}(2061, \cdot)$$ n/a 180 2
5780.2.r $$\chi_{5780}(3467, \cdot)$$ n/a 1564 2
5780.2.s $$\chi_{5780}(327, \cdot)$$ n/a 1564 2
5780.2.u $$\chi_{5780}(1001, \cdot)$$ n/a 360 4
5780.2.w $$\chi_{5780}(423, \cdot)$$ n/a 3128 4
5780.2.z $$\chi_{5780}(2467, \cdot)$$ n/a 3128 4
5780.2.bb $$\chi_{5780}(1889, \cdot)$$ n/a 536 4
5780.2.bd $$\chi_{5780}(513, \cdot)$$ n/a 1080 8
5780.2.bf $$\chi_{5780}(131, \cdot)$$ n/a 4320 8
5780.2.bg $$\chi_{5780}(1659, \cdot)$$ n/a 6256 8
5780.2.bi $$\chi_{5780}(653, \cdot)$$ n/a 1080 8
5780.2.bk $$\chi_{5780}(341, \cdot)$$ n/a 1632 16
5780.2.bm $$\chi_{5780}(169, \cdot)$$ n/a 2432 16
5780.2.bo $$\chi_{5780}(69, \cdot)$$ n/a 2432 16
5780.2.bq $$\chi_{5780}(101, \cdot)$$ n/a 1632 16
5780.2.bt $$\chi_{5780}(183, \cdot)$$ n/a 29248 32
5780.2.bu $$\chi_{5780}(67, \cdot)$$ n/a 29248 32
5780.2.bx $$\chi_{5780}(21, \cdot)$$ n/a 3264 32
5780.2.bz $$\chi_{5780}(89, \cdot)$$ n/a 4864 32
5780.2.ca $$\chi_{5780}(103, \cdot)$$ n/a 29248 32
5780.2.cd $$\chi_{5780}(47, \cdot)$$ n/a 29248 32
5780.2.ce $$\chi_{5780}(9, \cdot)$$ n/a 9856 64
5780.2.cg $$\chi_{5780}(43, \cdot)$$ n/a 58496 64
5780.2.cj $$\chi_{5780}(83, \cdot)$$ n/a 58496 64
5780.2.cl $$\chi_{5780}(121, \cdot)$$ n/a 6528 64
5780.2.cn $$\chi_{5780}(37, \cdot)$$ n/a 19584 128
5780.2.cp $$\chi_{5780}(39, \cdot)$$ n/a 116992 128
5780.2.cq $$\chi_{5780}(11, \cdot)$$ n/a 78336 128
5780.2.cs $$\chi_{5780}(57, \cdot)$$ n/a 19584 128

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5780))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5780)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(68))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(85))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(170))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(289))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(340))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(578))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1156))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1445))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2890))$$$$^{\oplus 2}$$