## Defining parameters

 Level: $$N$$ = $$6776 = 2^{3} \cdot 7 \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$5575680$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6776))$$.

Total New Old
Modular forms 1405440 741852 663588
Cusp forms 1382401 736232 646169
Eisenstein series 23039 5620 17419

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6776))$$

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
6776.2.a $$\chi_{6776}(1, \cdot)$$ 6776.2.a.a 1 1
6776.2.a.b 1
6776.2.a.c 1
6776.2.a.d 1
6776.2.a.e 1
6776.2.a.f 1
6776.2.a.g 1
6776.2.a.h 1
6776.2.a.i 1
6776.2.a.j 2
6776.2.a.k 2
6776.2.a.l 2
6776.2.a.m 2
6776.2.a.n 2
6776.2.a.o 2
6776.2.a.p 2
6776.2.a.q 2
6776.2.a.r 2
6776.2.a.s 2
6776.2.a.t 2
6776.2.a.u 3
6776.2.a.v 3
6776.2.a.w 3
6776.2.a.x 3
6776.2.a.y 3
6776.2.a.z 4
6776.2.a.ba 4
6776.2.a.bb 4
6776.2.a.bc 5
6776.2.a.bd 5
6776.2.a.be 6
6776.2.a.bf 6
6776.2.a.bg 6
6776.2.a.bh 6
6776.2.a.bi 8
6776.2.a.bj 8
6776.2.a.bk 8
6776.2.a.bl 8
6776.2.a.bm 10
6776.2.a.bn 10
6776.2.a.bo 10
6776.2.a.bp 10
6776.2.c $$\chi_{6776}(3389, \cdot)$$ n/a 654 1
6776.2.e $$\chi_{6776}(5081, \cdot)$$ n/a 216 1
6776.2.f $$\chi_{6776}(967, \cdot)$$ None 0 1
6776.2.h $$\chi_{6776}(4115, \cdot)$$ n/a 854 1
6776.2.j $$\chi_{6776}(727, \cdot)$$ None 0 1
6776.2.l $$\chi_{6776}(4355, \cdot)$$ n/a 648 1
6776.2.o $$\chi_{6776}(1693, \cdot)$$ n/a 848 1
6776.2.q $$\chi_{6776}(3873, \cdot)$$ n/a 436 2
6776.2.r $$\chi_{6776}(729, \cdot)$$ n/a 648 4
6776.2.s $$\chi_{6776}(3629, \cdot)$$ n/a 1696 2
6776.2.w $$\chi_{6776}(2663, \cdot)$$ None 0 2
6776.2.y $$\chi_{6776}(1451, \cdot)$$ n/a 1696 2
6776.2.ba $$\chi_{6776}(4839, \cdot)$$ None 0 2
6776.2.bc $$\chi_{6776}(243, \cdot)$$ n/a 1708 2
6776.2.bd $$\chi_{6776}(485, \cdot)$$ n/a 1708 2
6776.2.bf $$\chi_{6776}(241, \cdot)$$ n/a 432 2
6776.2.bi $$\chi_{6776}(965, \cdot)$$ n/a 3392 4
6776.2.bl $$\chi_{6776}(1443, \cdot)$$ n/a 2592 4
6776.2.bn $$\chi_{6776}(1455, \cdot)$$ None 0 4
6776.2.bp $$\chi_{6776}(27, \cdot)$$ n/a 3392 4
6776.2.br $$\chi_{6776}(239, \cdot)$$ None 0 4
6776.2.bs $$\chi_{6776}(2169, \cdot)$$ n/a 864 4
6776.2.bu $$\chi_{6776}(4117, \cdot)$$ n/a 2592 4
6776.2.bw $$\chi_{6776}(617, \cdot)$$ n/a 1980 10
6776.2.bx $$\chi_{6776}(9, \cdot)$$ n/a 1728 8
6776.2.bz $$\chi_{6776}(419, \cdot)$$ n/a 10520 10
6776.2.cb $$\chi_{6776}(351, \cdot)$$ None 0 10
6776.2.cc $$\chi_{6776}(153, \cdot)$$ n/a 2640 10
6776.2.ce $$\chi_{6776}(309, \cdot)$$ n/a 7920 10
6776.2.ch $$\chi_{6776}(461, \cdot)$$ n/a 10520 10
6776.2.ck $$\chi_{6776}(43, \cdot)$$ n/a 7920 10
6776.2.cm $$\chi_{6776}(111, \cdot)$$ None 0 10
6776.2.co $$\chi_{6776}(481, \cdot)$$ n/a 1728 8
6776.2.cq $$\chi_{6776}(1213, \cdot)$$ n/a 6784 8
6776.2.cr $$\chi_{6776}(3, \cdot)$$ n/a 6784 8
6776.2.ct $$\chi_{6776}(1927, \cdot)$$ None 0 8
6776.2.cv $$\chi_{6776}(403, \cdot)$$ n/a 6784 8
6776.2.cx $$\chi_{6776}(3391, \cdot)$$ None 0 8
6776.2.db $$\chi_{6776}(717, \cdot)$$ n/a 6784 8
6776.2.dc $$\chi_{6776}(177, \cdot)$$ n/a 5280 20
6776.2.dd $$\chi_{6776}(113, \cdot)$$ n/a 7920 40
6776.2.de $$\chi_{6776}(219, \cdot)$$ n/a 21040 20
6776.2.dg $$\chi_{6776}(199, \cdot)$$ None 0 20
6776.2.dk $$\chi_{6776}(285, \cdot)$$ n/a 21040 20
6776.2.dm $$\chi_{6776}(593, \cdot)$$ n/a 5280 20
6776.2.do $$\chi_{6776}(221, \cdot)$$ n/a 21040 20
6776.2.dp $$\chi_{6776}(507, \cdot)$$ n/a 21040 20
6776.2.dr $$\chi_{6776}(263, \cdot)$$ None 0 20
6776.2.dt $$\chi_{6776}(223, \cdot)$$ None 0 40
6776.2.dv $$\chi_{6776}(211, \cdot)$$ n/a 31680 40
6776.2.dy $$\chi_{6776}(13, \cdot)$$ n/a 42080 40
6776.2.eb $$\chi_{6776}(141, \cdot)$$ n/a 31680 40
6776.2.ed $$\chi_{6776}(41, \cdot)$$ n/a 10560 40
6776.2.ee $$\chi_{6776}(127, \cdot)$$ None 0 40
6776.2.eg $$\chi_{6776}(531, \cdot)$$ n/a 42080 40
6776.2.ei $$\chi_{6776}(25, \cdot)$$ n/a 21120 80
6776.2.ek $$\chi_{6776}(39, \cdot)$$ None 0 80
6776.2.em $$\chi_{6776}(59, \cdot)$$ n/a 84160 80
6776.2.en $$\chi_{6776}(37, \cdot)$$ n/a 84160 80
6776.2.ep $$\chi_{6776}(17, \cdot)$$ n/a 21120 80
6776.2.er $$\chi_{6776}(61, \cdot)$$ n/a 84160 80
6776.2.ev $$\chi_{6776}(31, \cdot)$$ None 0 80
6776.2.ex $$\chi_{6776}(51, \cdot)$$ n/a 84160 80

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6776))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6776)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(242))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(308))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(484))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(616))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(847))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(968))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1694))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3388))$$$$^{\oplus 2}$$