# Properties

 Label 6960.2 Level 6960 Weight 2 Dimension 496316 Nonzero newspaces 104 Sturm bound 5160960

## Defining parameters

 Level: $$N$$ = $$6960 = 2^{4} \cdot 3 \cdot 5 \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$104$$ Sturm bound: $$5160960$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6960))$$.

Total New Old
Modular forms 1302784 499228 803556
Cusp forms 1277697 496316 781381
Eisenstein series 25087 2912 22175

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6960))$$

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
6960.2.a $$\chi_{6960}(1, \cdot)$$ 6960.2.a.a 1 1
6960.2.a.b 1
6960.2.a.c 1
6960.2.a.d 1
6960.2.a.e 1
6960.2.a.f 1
6960.2.a.g 1
6960.2.a.h 1
6960.2.a.i 1
6960.2.a.j 1
6960.2.a.k 1
6960.2.a.l 1
6960.2.a.m 1
6960.2.a.n 1
6960.2.a.o 1
6960.2.a.p 1
6960.2.a.q 1
6960.2.a.r 1
6960.2.a.s 1
6960.2.a.t 1
6960.2.a.u 1
6960.2.a.v 1
6960.2.a.w 1
6960.2.a.x 1
6960.2.a.y 1
6960.2.a.z 1
6960.2.a.ba 1
6960.2.a.bb 1
6960.2.a.bc 1
6960.2.a.bd 1
6960.2.a.be 1
6960.2.a.bf 1
6960.2.a.bg 1
6960.2.a.bh 1
6960.2.a.bi 1
6960.2.a.bj 1
6960.2.a.bk 1
6960.2.a.bl 1
6960.2.a.bm 1
6960.2.a.bn 1
6960.2.a.bo 1
6960.2.a.bp 2
6960.2.a.bq 2
6960.2.a.br 2
6960.2.a.bs 2
6960.2.a.bt 2
6960.2.a.bu 2
6960.2.a.bv 2
6960.2.a.bw 2
6960.2.a.bx 2
6960.2.a.by 2
6960.2.a.bz 2
6960.2.a.ca 2
6960.2.a.cb 2
6960.2.a.cc 2
6960.2.a.cd 2
6960.2.a.ce 2
6960.2.a.cf 2
6960.2.a.cg 2
6960.2.a.ch 2
6960.2.a.ci 2
6960.2.a.cj 3
6960.2.a.ck 3
6960.2.a.cl 3
6960.2.a.cm 4
6960.2.a.cn 4
6960.2.a.co 4
6960.2.a.cp 5
6960.2.a.cq 5
6960.2.c $$\chi_{6960}(3191, \cdot)$$ None 0 1
6960.2.d $$\chi_{6960}(289, \cdot)$$ n/a 180 1
6960.2.f $$\chi_{6960}(2089, \cdot)$$ None 0 1
6960.2.i $$\chi_{6960}(1391, \cdot)$$ n/a 240 1
6960.2.k $$\chi_{6960}(5569, \cdot)$$ n/a 168 1
6960.2.l $$\chi_{6960}(4871, \cdot)$$ None 0 1
6960.2.n $$\chi_{6960}(6671, \cdot)$$ n/a 224 1
6960.2.q $$\chi_{6960}(3769, \cdot)$$ None 0 1
6960.2.s $$\chi_{6960}(6959, \cdot)$$ n/a 360 1
6960.2.t $$\chi_{6960}(3481, \cdot)$$ None 0 1
6960.2.v $$\chi_{6960}(1681, \cdot)$$ n/a 120 1
6960.2.y $$\chi_{6960}(1799, \cdot)$$ None 0 1
6960.2.ba $$\chi_{6960}(5161, \cdot)$$ None 0 1
6960.2.bb $$\chi_{6960}(5279, \cdot)$$ n/a 336 1
6960.2.bd $$\chi_{6960}(3479, \cdot)$$ None 0 1
6960.2.bh $$\chi_{6960}(1061, \cdot)$$ n/a 1920 2
6960.2.bj $$\chi_{6960}(2419, \cdot)$$ n/a 1440 2
6960.2.bl $$\chi_{6960}(4831, \cdot)$$ n/a 240 2
6960.2.bm $$\chi_{6960}(4889, \cdot)$$ None 0 2
6960.2.bp $$\chi_{6960}(3421, \cdot)$$ n/a 960 2
6960.2.bq $$\chi_{6960}(1739, \cdot)$$ n/a 2864 2
6960.2.bs $$\chi_{6960}(1741, \cdot)$$ n/a 896 2
6960.2.bv $$\chi_{6960}(59, \cdot)$$ n/a 2688 2
6960.2.bw $$\chi_{6960}(1351, \cdot)$$ None 0 2
6960.2.bz $$\chi_{6960}(1409, \cdot)$$ n/a 712 2
6960.2.ca $$\chi_{6960}(1699, \cdot)$$ n/a 1440 2
6960.2.cc $$\chi_{6960}(1781, \cdot)$$ n/a 1920 2
6960.2.cf $$\chi_{6960}(2627, \cdot)$$ n/a 2864 2
6960.2.cg $$\chi_{6960}(853, \cdot)$$ n/a 1440 2
6960.2.cj $$\chi_{6960}(1913, \cdot)$$ None 0 2
6960.2.ck $$\chi_{6960}(3713, \cdot)$$ n/a 672 2
6960.2.cn $$\chi_{6960}(1567, \cdot)$$ n/a 336 2
6960.2.co $$\chi_{6960}(3943, \cdot)$$ None 0 2
6960.2.cq $$\chi_{6960}(3613, \cdot)$$ n/a 1440 2
6960.2.ct $$\chi_{6960}(6803, \cdot)$$ n/a 2864 2
6960.2.cu $$\chi_{6960}(3307, \cdot)$$ n/a 1344 2
6960.2.cw $$\chi_{6960}(173, \cdot)$$ n/a 2864 2
6960.2.cz $$\chi_{6960}(4757, \cdot)$$ n/a 2688 2
6960.2.db $$\chi_{6960}(4987, \cdot)$$ n/a 1440 2
6960.2.dc $$\chi_{6960}(1897, \cdot)$$ None 0 2
6960.2.de $$\chi_{6960}(2303, \cdot)$$ n/a 720 2
6960.2.dg $$\chi_{6960}(887, \cdot)$$ None 0 2
6960.2.di $$\chi_{6960}(1873, \cdot)$$ n/a 360 2
6960.2.dk $$\chi_{6960}(2593, \cdot)$$ n/a 360 2
6960.2.dm $$\chi_{6960}(1607, \cdot)$$ None 0 2
6960.2.do $$\chi_{6960}(1583, \cdot)$$ n/a 720 2
6960.2.dq $$\chi_{6960}(1177, \cdot)$$ None 0 2
6960.2.ds $$\chi_{6960}(2957, \cdot)$$ n/a 2864 2
6960.2.du $$\chi_{6960}(523, \cdot)$$ n/a 1344 2
6960.2.dx $$\chi_{6960}(1507, \cdot)$$ n/a 1440 2
6960.2.dz $$\chi_{6960}(1277, \cdot)$$ n/a 2688 2
6960.2.eb $$\chi_{6960}(133, \cdot)$$ n/a 1440 2
6960.2.ec $$\chi_{6960}(3323, \cdot)$$ n/a 2864 2
6960.2.ef $$\chi_{6960}(2263, \cdot)$$ None 0 2
6960.2.eg $$\chi_{6960}(463, \cdot)$$ n/a 360 2
6960.2.ej $$\chi_{6960}(1217, \cdot)$$ n/a 712 2
6960.2.ek $$\chi_{6960}(233, \cdot)$$ None 0 2
6960.2.em $$\chi_{6960}(563, \cdot)$$ n/a 2864 2
6960.2.ep $$\chi_{6960}(2917, \cdot)$$ n/a 1440 2
6960.2.eq $$\chi_{6960}(3869, \cdot)$$ n/a 2864 2
6960.2.es $$\chi_{6960}(3811, \cdot)$$ n/a 960 2
6960.2.eu $$\chi_{6960}(2801, \cdot)$$ n/a 480 2
6960.2.ex $$\chi_{6960}(679, \cdot)$$ None 0 2
6960.2.ez $$\chi_{6960}(1451, \cdot)$$ n/a 1792 2
6960.2.fa $$\chi_{6960}(349, \cdot)$$ n/a 1344 2
6960.2.fc $$\chi_{6960}(3131, \cdot)$$ n/a 1920 2
6960.2.ff $$\chi_{6960}(2029, \cdot)$$ n/a 1440 2
6960.2.fh $$\chi_{6960}(41, \cdot)$$ None 0 2
6960.2.fi $$\chi_{6960}(3439, \cdot)$$ n/a 360 2
6960.2.fl $$\chi_{6960}(331, \cdot)$$ n/a 960 2
6960.2.fn $$\chi_{6960}(389, \cdot)$$ n/a 2864 2
6960.2.fo $$\chi_{6960}(721, \cdot)$$ n/a 720 6
6960.2.fq $$\chi_{6960}(1079, \cdot)$$ None 0 6
6960.2.fs $$\chi_{6960}(121, \cdot)$$ None 0 6
6960.2.fv $$\chi_{6960}(239, \cdot)$$ n/a 2160 6
6960.2.fx $$\chi_{6960}(241, \cdot)$$ n/a 720 6
6960.2.fy $$\chi_{6960}(2519, \cdot)$$ None 0 6
6960.2.ga $$\chi_{6960}(1919, \cdot)$$ n/a 2160 6
6960.2.gd $$\chi_{6960}(1321, \cdot)$$ None 0 6
6960.2.gf $$\chi_{6960}(431, \cdot)$$ n/a 1440 6
6960.2.gg $$\chi_{6960}(1369, \cdot)$$ None 0 6
6960.2.gi $$\chi_{6960}(49, \cdot)$$ n/a 1080 6
6960.2.gl $$\chi_{6960}(71, \cdot)$$ None 0 6
6960.2.gn $$\chi_{6960}(169, \cdot)$$ None 0 6
6960.2.go $$\chi_{6960}(671, \cdot)$$ n/a 1440 6
6960.2.gq $$\chi_{6960}(1031, \cdot)$$ None 0 6
6960.2.gt $$\chi_{6960}(2209, \cdot)$$ n/a 1080 6
6960.2.gu $$\chi_{6960}(989, \cdot)$$ n/a 17184 12
6960.2.gw $$\chi_{6960}(931, \cdot)$$ n/a 5760 12
6960.2.gz $$\chi_{6960}(79, \cdot)$$ n/a 2160 12
6960.2.ha $$\chi_{6960}(1001, \cdot)$$ None 0 12
6960.2.hc $$\chi_{6960}(1069, \cdot)$$ n/a 8640 12
6960.2.hf $$\chi_{6960}(371, \cdot)$$ n/a 11520 12
6960.2.hh $$\chi_{6960}(109, \cdot)$$ n/a 8640 12
6960.2.hi $$\chi_{6960}(731, \cdot)$$ n/a 11520 12
6960.2.hk $$\chi_{6960}(1639, \cdot)$$ None 0 12
6960.2.hn $$\chi_{6960}(641, \cdot)$$ n/a 2880 12
6960.2.hp $$\chi_{6960}(211, \cdot)$$ n/a 5760 12
6960.2.hr $$\chi_{6960}(269, \cdot)$$ n/a 17184 12
6960.2.ht $$\chi_{6960}(1307, \cdot)$$ n/a 17184 12
6960.2.hu $$\chi_{6960}(733, \cdot)$$ n/a 8640 12
6960.2.hw $$\chi_{6960}(857, \cdot)$$ None 0 12
6960.2.hz $$\chi_{6960}(353, \cdot)$$ n/a 4272 12
6960.2.ia $$\chi_{6960}(847, \cdot)$$ n/a 2160 12
6960.2.id $$\chi_{6960}(7, \cdot)$$ None 0 12
6960.2.ie $$\chi_{6960}(1117, \cdot)$$ n/a 8640 12
6960.2.ih $$\chi_{6960}(1163, \cdot)$$ n/a 17184 12
6960.2.ij $$\chi_{6960}(53, \cdot)$$ n/a 17184 12
6960.2.il $$\chi_{6960}(67, \cdot)$$ n/a 8640 12
6960.2.im $$\chi_{6960}(547, \cdot)$$ n/a 8640 12
6960.2.io $$\chi_{6960}(557, \cdot)$$ n/a 17184 12
6960.2.ir $$\chi_{6960}(97, \cdot)$$ n/a 2160 12
6960.2.it $$\chi_{6960}(503, \cdot)$$ None 0 12
6960.2.iv $$\chi_{6960}(143, \cdot)$$ n/a 4320 12
6960.2.ix $$\chi_{6960}(553, \cdot)$$ None 0 12
6960.2.iz $$\chi_{6960}(73, \cdot)$$ None 0 12
6960.2.jb $$\chi_{6960}(47, \cdot)$$ n/a 4320 12
6960.2.jd $$\chi_{6960}(263, \cdot)$$ None 0 12
6960.2.jf $$\chi_{6960}(433, \cdot)$$ n/a 2160 12
6960.2.jh $$\chi_{6960}(187, \cdot)$$ n/a 8640 12
6960.2.jj $$\chi_{6960}(197, \cdot)$$ n/a 17184 12
6960.2.jk $$\chi_{6960}(1397, \cdot)$$ n/a 17184 12
6960.2.jm $$\chi_{6960}(1147, \cdot)$$ n/a 8640 12
6960.2.jp $$\chi_{6960}(37, \cdot)$$ n/a 8640 12
6960.2.jq $$\chi_{6960}(827, \cdot)$$ n/a 17184 12
6960.2.js $$\chi_{6960}(1543, \cdot)$$ None 0 12
6960.2.jv $$\chi_{6960}(223, \cdot)$$ n/a 2160 12
6960.2.jw $$\chi_{6960}(257, \cdot)$$ n/a 4272 12
6960.2.jz $$\chi_{6960}(473, \cdot)$$ None 0 12
6960.2.ka $$\chi_{6960}(443, \cdot)$$ n/a 17184 12
6960.2.kd $$\chi_{6960}(1597, \cdot)$$ n/a 8640 12
6960.2.kf $$\chi_{6960}(1181, \cdot)$$ n/a 11520 12
6960.2.kh $$\chi_{6960}(19, \cdot)$$ n/a 8640 12
6960.2.ki $$\chi_{6960}(449, \cdot)$$ n/a 4272 12
6960.2.kl $$\chi_{6960}(391, \cdot)$$ None 0 12
6960.2.km $$\chi_{6960}(179, \cdot)$$ n/a 17184 12
6960.2.kp $$\chi_{6960}(1021, \cdot)$$ n/a 5760 12
6960.2.kr $$\chi_{6960}(779, \cdot)$$ n/a 17184 12
6960.2.ks $$\chi_{6960}(181, \cdot)$$ n/a 5760 12
6960.2.kv $$\chi_{6960}(89, \cdot)$$ None 0 12
6960.2.kw $$\chi_{6960}(31, \cdot)$$ n/a 1440 12
6960.2.ky $$\chi_{6960}(259, \cdot)$$ n/a 8640 12
6960.2.la $$\chi_{6960}(101, \cdot)$$ n/a 11520 12

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6960))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6960)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 40}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 32}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(58))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(87))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(116))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(145))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(174))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(232))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(240))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(290))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(348))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(435))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(464))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(580))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(696))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(870))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1160))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1392))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1740))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2320))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3480))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6960))$$$$^{\oplus 1}$$