# Properties

 Label 5776.2 Level 5776 Weight 2 Dimension 579476 Nonzero newspaces 24 Sturm bound 4158720

## Defining parameters

 Level: $$N$$ = $$5776 = 2^{4} \cdot 19^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$4158720$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5776))$$.

Total New Old
Modular forms 1046736 583693 463043
Cusp forms 1032625 579476 453149
Eisenstein series 14111 4217 9894

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5776))$$

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
5776.2.a $$\chi_{5776}(1, \cdot)$$ 5776.2.a.a 1 1
5776.2.a.b 1
5776.2.a.c 1
5776.2.a.d 1
5776.2.a.e 1
5776.2.a.f 1
5776.2.a.g 1
5776.2.a.h 1
5776.2.a.i 1
5776.2.a.j 1
5776.2.a.k 1
5776.2.a.l 1
5776.2.a.m 1
5776.2.a.n 1
5776.2.a.o 1
5776.2.a.p 1
5776.2.a.q 1
5776.2.a.r 2
5776.2.a.s 2
5776.2.a.t 2
5776.2.a.u 2
5776.2.a.v 2
5776.2.a.w 2
5776.2.a.x 2
5776.2.a.y 2
5776.2.a.z 2
5776.2.a.ba 2
5776.2.a.bb 2
5776.2.a.bc 2
5776.2.a.bd 2
5776.2.a.be 2
5776.2.a.bf 2
5776.2.a.bg 2
5776.2.a.bh 2
5776.2.a.bi 3
5776.2.a.bj 3
5776.2.a.bk 3
5776.2.a.bl 3
5776.2.a.bm 3
5776.2.a.bn 3
5776.2.a.bo 3
5776.2.a.bp 3
5776.2.a.bq 3
5776.2.a.br 3
5776.2.a.bs 3
5776.2.a.bt 4
5776.2.a.bu 4
5776.2.a.bv 4
5776.2.a.bw 6
5776.2.a.bx 6
5776.2.a.by 6
5776.2.a.bz 6
5776.2.a.ca 8
5776.2.a.cb 8
5776.2.a.cc 8
5776.2.a.cd 9
5776.2.a.ce 9
5776.2.b $$\chi_{5776}(2887, \cdot)$$ None 0 1
5776.2.c $$\chi_{5776}(2889, \cdot)$$ None 0 1
5776.2.h $$\chi_{5776}(5775, \cdot)$$ n/a 170 1
5776.2.i $$\chi_{5776}(1873, \cdot)$$ n/a 324 2
5776.2.k $$\chi_{5776}(1445, \cdot)$$ n/a 1330 2
5776.2.m $$\chi_{5776}(1443, \cdot)$$ n/a 1328 2
5776.2.n $$\chi_{5776}(3679, \cdot)$$ n/a 340 2
5776.2.s $$\chi_{5776}(791, \cdot)$$ None 0 2
5776.2.t $$\chi_{5776}(4761, \cdot)$$ None 0 2
5776.2.u $$\chi_{5776}(1137, \cdot)$$ n/a 972 6
5776.2.v $$\chi_{5776}(429, \cdot)$$ n/a 2656 4
5776.2.x $$\chi_{5776}(2235, \cdot)$$ n/a 2656 4
5776.2.bb $$\chi_{5776}(1145, \cdot)$$ None 0 6
5776.2.bd $$\chi_{5776}(1751, \cdot)$$ None 0 6
5776.2.be $$\chi_{5776}(127, \cdot)$$ n/a 1020 6
5776.2.bg $$\chi_{5776}(305, \cdot)$$ n/a 3402 18
5776.2.bh $$\chi_{5776}(299, \cdot)$$ n/a 7968 12
5776.2.bj $$\chi_{5776}(245, \cdot)$$ n/a 7968 12
5776.2.bl $$\chi_{5776}(303, \cdot)$$ n/a 3420 18
5776.2.bq $$\chi_{5776}(153, \cdot)$$ None 0 18
5776.2.br $$\chi_{5776}(151, \cdot)$$ None 0 18
5776.2.bs $$\chi_{5776}(49, \cdot)$$ n/a 6804 36
5776.2.bt $$\chi_{5776}(75, \cdot)$$ n/a 27288 36
5776.2.bv $$\chi_{5776}(77, \cdot)$$ n/a 27288 36
5776.2.bx $$\chi_{5776}(121, \cdot)$$ None 0 36
5776.2.by $$\chi_{5776}(103, \cdot)$$ None 0 36
5776.2.cd $$\chi_{5776}(31, \cdot)$$ n/a 6840 36
5776.2.ce $$\chi_{5776}(17, \cdot)$$ n/a 20412 108
5776.2.cg $$\chi_{5776}(27, \cdot)$$ n/a 54576 72
5776.2.ci $$\chi_{5776}(45, \cdot)$$ n/a 54576 72
5776.2.ck $$\chi_{5776}(15, \cdot)$$ n/a 20520 108
5776.2.cl $$\chi_{5776}(71, \cdot)$$ None 0 108
5776.2.cn $$\chi_{5776}(9, \cdot)$$ None 0 108
5776.2.cr $$\chi_{5776}(5, \cdot)$$ n/a 163728 216
5776.2.ct $$\chi_{5776}(3, \cdot)$$ n/a 163728 216

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5776))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5776)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(361))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(722))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1444))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2888))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5776))$$$$^{\oplus 1}$$