## Defining parameters

 Level: $$N$$ = $$5577 = 3 \cdot 11 \cdot 13^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$4542720$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5577))$$.

Total New Old
Modular forms 1144800 831362 313438
Cusp forms 1126561 823998 302563
Eisenstein series 18239 7364 10875

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5577))$$

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
5577.2.a $$\chi_{5577}(1, \cdot)$$ 5577.2.a.a 1 1
5577.2.a.b 1
5577.2.a.c 1
5577.2.a.d 1
5577.2.a.e 1
5577.2.a.f 1
5577.2.a.g 1
5577.2.a.h 2
5577.2.a.i 2
5577.2.a.j 3
5577.2.a.k 3
5577.2.a.l 3
5577.2.a.m 4
5577.2.a.n 5
5577.2.a.o 5
5577.2.a.p 5
5577.2.a.q 5
5577.2.a.r 5
5577.2.a.s 5
5577.2.a.t 5
5577.2.a.u 5
5577.2.a.v 5
5577.2.a.w 5
5577.2.a.x 7
5577.2.a.y 7
5577.2.a.z 12
5577.2.a.ba 12
5577.2.a.bb 12
5577.2.a.bc 12
5577.2.a.bd 12
5577.2.a.be 12
5577.2.a.bf 14
5577.2.a.bg 14
5577.2.a.bh 18
5577.2.a.bi 18
5577.2.a.bj 18
5577.2.a.bk 18
5577.2.b $$\chi_{5577}(2872, \cdot)$$ n/a 256 1
5577.2.e $$\chi_{5577}(5576, \cdot)$$ n/a 596 1
5577.2.f $$\chi_{5577}(2705, \cdot)$$ n/a 598 1
5577.2.i $$\chi_{5577}(529, \cdot)$$ n/a 516 2
5577.2.j $$\chi_{5577}(2267, \cdot)$$ n/a 1024 2
5577.2.m $$\chi_{5577}(3112, \cdot)$$ n/a 616 2
5577.2.n $$\chi_{5577}(1015, \cdot)$$ n/a 1240 4
5577.2.p $$\chi_{5577}(3233, \cdot)$$ n/a 1192 2
5577.2.s $$\chi_{5577}(1882, \cdot)$$ n/a 508 2
5577.2.t $$\chi_{5577}(4586, \cdot)$$ n/a 1192 2
5577.2.x $$\chi_{5577}(677, \cdot)$$ n/a 2392 4
5577.2.y $$\chi_{5577}(1520, \cdot)$$ n/a 2384 4
5577.2.bb $$\chi_{5577}(1351, \cdot)$$ n/a 1232 4
5577.2.bd $$\chi_{5577}(934, \cdot)$$ n/a 1232 4
5577.2.be $$\chi_{5577}(89, \cdot)$$ n/a 2056 4
5577.2.bg $$\chi_{5577}(430, \cdot)$$ n/a 3600 12
5577.2.bh $$\chi_{5577}(1543, \cdot)$$ n/a 2464 8
5577.2.bj $$\chi_{5577}(746, \cdot)$$ n/a 4768 8
5577.2.bk $$\chi_{5577}(1084, \cdot)$$ n/a 2464 8
5577.2.bo $$\chi_{5577}(131, \cdot)$$ n/a 8688 12
5577.2.bp $$\chi_{5577}(428, \cdot)$$ n/a 8688 12
5577.2.bs $$\chi_{5577}(298, \cdot)$$ n/a 3648 12
5577.2.bu $$\chi_{5577}(530, \cdot)$$ n/a 4768 8
5577.2.bv $$\chi_{5577}(361, \cdot)$$ n/a 2464 8
5577.2.by $$\chi_{5577}(1205, \cdot)$$ n/a 4768 8
5577.2.ca $$\chi_{5577}(100, \cdot)$$ n/a 7248 24
5577.2.cb $$\chi_{5577}(109, \cdot)$$ n/a 8736 24
5577.2.ce $$\chi_{5577}(122, \cdot)$$ n/a 14592 24
5577.2.cf $$\chi_{5577}(19, \cdot)$$ n/a 4928 16
5577.2.ci $$\chi_{5577}(80, \cdot)$$ n/a 9536 16
5577.2.cj $$\chi_{5577}(157, \cdot)$$ n/a 17472 48
5577.2.cl $$\chi_{5577}(296, \cdot)$$ n/a 17376 24
5577.2.cm $$\chi_{5577}(166, \cdot)$$ n/a 7344 24
5577.2.cp $$\chi_{5577}(230, \cdot)$$ n/a 17376 24
5577.2.cr $$\chi_{5577}(25, \cdot)$$ n/a 17472 48
5577.2.cu $$\chi_{5577}(116, \cdot)$$ n/a 34752 48
5577.2.cv $$\chi_{5577}(248, \cdot)$$ n/a 34752 48
5577.2.cz $$\chi_{5577}(254, \cdot)$$ n/a 29088 48
5577.2.da $$\chi_{5577}(76, \cdot)$$ n/a 17472 48
5577.2.dc $$\chi_{5577}(16, \cdot)$$ n/a 34944 96
5577.2.de $$\chi_{5577}(73, \cdot)$$ n/a 34944 96
5577.2.df $$\chi_{5577}(5, \cdot)$$ n/a 69504 96
5577.2.di $$\chi_{5577}(29, \cdot)$$ n/a 69504 96
5577.2.dl $$\chi_{5577}(4, \cdot)$$ n/a 34944 96
5577.2.dm $$\chi_{5577}(17, \cdot)$$ n/a 69504 96
5577.2.do $$\chi_{5577}(20, \cdot)$$ n/a 139008 192
5577.2.dr $$\chi_{5577}(7, \cdot)$$ n/a 69888 192

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5577))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5577)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(143))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(429))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(507))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1859))$$$$^{\oplus 2}$$