# Properties

 Label 6760.2 Level 6760 Weight 2 Dimension 691957 Nonzero newspaces 64 Sturm bound 5451264

## Defining parameters

 Level: $$N$$ = $$6760 = 2^{3} \cdot 5 \cdot 13^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$64$$ Sturm bound: $$5451264$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6760))$$.

Total New Old
Modular forms 1373760 696865 676895
Cusp forms 1351873 691957 659916
Eisenstein series 21887 4908 16979

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6760))$$

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
6760.2.a $$\chi_{6760}(1, \cdot)$$ 6760.2.a.a 1 1
6760.2.a.b 1
6760.2.a.c 1
6760.2.a.d 1
6760.2.a.e 1
6760.2.a.f 1
6760.2.a.g 1
6760.2.a.h 1
6760.2.a.i 1
6760.2.a.j 1
6760.2.a.k 1
6760.2.a.l 1
6760.2.a.m 1
6760.2.a.n 2
6760.2.a.o 2
6760.2.a.p 2
6760.2.a.q 2
6760.2.a.r 2
6760.2.a.s 2
6760.2.a.t 2
6760.2.a.u 3
6760.2.a.v 3
6760.2.a.w 3
6760.2.a.x 3
6760.2.a.y 3
6760.2.a.z 3
6760.2.a.ba 4
6760.2.a.bb 4
6760.2.a.bc 4
6760.2.a.bd 4
6760.2.a.be 6
6760.2.a.bf 6
6760.2.a.bg 6
6760.2.a.bh 6
6760.2.a.bi 6
6760.2.a.bj 6
6760.2.a.bk 8
6760.2.a.bl 8
6760.2.a.bm 9
6760.2.a.bn 9
6760.2.a.bo 12
6760.2.a.bp 12
6760.2.d $$\chi_{6760}(5409, \cdot)$$ n/a 232 1
6760.2.e $$\chi_{6760}(6421, \cdot)$$ n/a 616 1
6760.2.f $$\chi_{6760}(1689, \cdot)$$ n/a 232 1
6760.2.g $$\chi_{6760}(3381, \cdot)$$ n/a 620 1
6760.2.j $$\chi_{6760}(2029, \cdot)$$ n/a 908 1
6760.2.k $$\chi_{6760}(3041, \cdot)$$ n/a 154 1
6760.2.p $$\chi_{6760}(5069, \cdot)$$ n/a 904 1
6760.2.q $$\chi_{6760}(1881, \cdot)$$ n/a 308 2
6760.2.s $$\chi_{6760}(1591, \cdot)$$ None 0 2
6760.2.t $$\chi_{6760}(99, \cdot)$$ n/a 1808 2
6760.2.w $$\chi_{6760}(577, \cdot)$$ n/a 462 2
6760.2.y $$\chi_{6760}(3957, \cdot)$$ n/a 1808 2
6760.2.bb $$\chi_{6760}(2367, \cdot)$$ None 0 2
6760.2.bc $$\chi_{6760}(2027, \cdot)$$ n/a 1808 2
6760.2.bd $$\chi_{6760}(2703, \cdot)$$ None 0 2
6760.2.be $$\chi_{6760}(3043, \cdot)$$ n/a 1816 2
6760.2.bh $$\chi_{6760}(3817, \cdot)$$ n/a 462 2
6760.2.bj $$\chi_{6760}(437, \cdot)$$ n/a 1808 2
6760.2.bm $$\chi_{6760}(1451, \cdot)$$ n/a 1232 2
6760.2.bn $$\chi_{6760}(239, \cdot)$$ None 0 2
6760.2.bp $$\chi_{6760}(2389, \cdot)$$ n/a 1808 2
6760.2.bu $$\chi_{6760}(361, \cdot)$$ n/a 308 2
6760.2.bv $$\chi_{6760}(3909, \cdot)$$ n/a 1808 2
6760.2.by $$\chi_{6760}(5261, \cdot)$$ n/a 1232 2
6760.2.bz $$\chi_{6760}(5769, \cdot)$$ n/a 464 2
6760.2.ca $$\chi_{6760}(3741, \cdot)$$ n/a 1232 2
6760.2.cb $$\chi_{6760}(529, \cdot)$$ n/a 460 2
6760.2.cf $$\chi_{6760}(319, \cdot)$$ None 0 4
6760.2.cg $$\chi_{6760}(1371, \cdot)$$ n/a 2464 4
6760.2.cj $$\chi_{6760}(2117, \cdot)$$ n/a 3616 4
6760.2.cl $$\chi_{6760}(657, \cdot)$$ n/a 924 4
6760.2.cm $$\chi_{6760}(867, \cdot)$$ n/a 3616 4
6760.2.cn $$\chi_{6760}(23, \cdot)$$ None 0 4
6760.2.cs $$\chi_{6760}(147, \cdot)$$ n/a 3616 4
6760.2.ct $$\chi_{6760}(1543, \cdot)$$ None 0 4
6760.2.cu $$\chi_{6760}(357, \cdot)$$ n/a 3616 4
6760.2.cw $$\chi_{6760}(2793, \cdot)$$ n/a 924 4
6760.2.cz $$\chi_{6760}(19, \cdot)$$ n/a 3616 4
6760.2.da $$\chi_{6760}(1671, \cdot)$$ None 0 4
6760.2.dc $$\chi_{6760}(521, \cdot)$$ n/a 2184 12
6760.2.dd $$\chi_{6760}(389, \cdot)$$ n/a 13056 12
6760.2.di $$\chi_{6760}(441, \cdot)$$ n/a 2184 12
6760.2.dj $$\chi_{6760}(469, \cdot)$$ n/a 13056 12
6760.2.dm $$\chi_{6760}(261, \cdot)$$ n/a 8736 12
6760.2.dn $$\chi_{6760}(129, \cdot)$$ n/a 3264 12
6760.2.do $$\chi_{6760}(181, \cdot)$$ n/a 8736 12
6760.2.dp $$\chi_{6760}(209, \cdot)$$ n/a 3288 12
6760.2.ds $$\chi_{6760}(81, \cdot)$$ n/a 4368 24
6760.2.dt $$\chi_{6760}(359, \cdot)$$ None 0 24
6760.2.dw $$\chi_{6760}(291, \cdot)$$ n/a 17472 24
6760.2.dy $$\chi_{6760}(213, \cdot)$$ n/a 26112 24
6760.2.ea $$\chi_{6760}(177, \cdot)$$ n/a 6552 24
6760.2.ed $$\chi_{6760}(27, \cdot)$$ n/a 26112 24
6760.2.ee $$\chi_{6760}(103, \cdot)$$ None 0 24
6760.2.ef $$\chi_{6760}(363, \cdot)$$ n/a 26112 24
6760.2.eg $$\chi_{6760}(183, \cdot)$$ None 0 24
6760.2.ej $$\chi_{6760}(317, \cdot)$$ n/a 26112 24
6760.2.el $$\chi_{6760}(57, \cdot)$$ n/a 6552 24
6760.2.en $$\chi_{6760}(499, \cdot)$$ n/a 26112 24
6760.2.eq $$\chi_{6760}(31, \cdot)$$ None 0 24
6760.2.et $$\chi_{6760}(9, \cdot)$$ n/a 6576 24
6760.2.eu $$\chi_{6760}(101, \cdot)$$ n/a 17472 24
6760.2.ev $$\chi_{6760}(49, \cdot)$$ n/a 6528 24
6760.2.ew $$\chi_{6760}(61, \cdot)$$ n/a 17472 24
6760.2.ez $$\chi_{6760}(29, \cdot)$$ n/a 26112 24
6760.2.fa $$\chi_{6760}(121, \cdot)$$ n/a 4368 24
6760.2.ff $$\chi_{6760}(69, \cdot)$$ n/a 26112 24
6760.2.fg $$\chi_{6760}(71, \cdot)$$ None 0 48
6760.2.fj $$\chi_{6760}(59, \cdot)$$ n/a 52224 48
6760.2.fl $$\chi_{6760}(33, \cdot)$$ n/a 13104 48
6760.2.fn $$\chi_{6760}(197, \cdot)$$ n/a 52224 48
6760.2.fo $$\chi_{6760}(87, \cdot)$$ None 0 48
6760.2.fp $$\chi_{6760}(43, \cdot)$$ n/a 52224 48
6760.2.fu $$\chi_{6760}(127, \cdot)$$ None 0 48
6760.2.fv $$\chi_{6760}(3, \cdot)$$ n/a 52224 48
6760.2.fw $$\chi_{6760}(137, \cdot)$$ n/a 13104 48
6760.2.fy $$\chi_{6760}(37, \cdot)$$ n/a 52224 48
6760.2.ga $$\chi_{6760}(11, \cdot)$$ n/a 34944 48
6760.2.gd $$\chi_{6760}(119, \cdot)$$ None 0 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6760))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6760)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(130))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(260))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(338))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(520))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(676))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(845))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1352))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1690))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3380))$$$$^{\oplus 2}$$