Properties

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

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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

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