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Properties

Label 8976.2
Level 8976
Weight 2
Dimension 908768
Nonzero newspaces 104
Sturm bound 8847360

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Defining parameters

Level: \( N \) = \( 8976 = 2^{4} \cdot 3 \cdot 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 104 \)
Sturm bound: \(8847360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8976))\).

Total New Old
Modular forms 2229760 913624 1316136
Cusp forms 2193921 908768 1285153
Eisenstein series 35839 4856 30983

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8976))\)

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
8976.2.a \(\chi_{8976}(1, \cdot)\) 8976.2.a.a 1 1
8976.2.a.b 1
8976.2.a.c 1
8976.2.a.d 1
8976.2.a.e 1
8976.2.a.f 1
8976.2.a.g 1
8976.2.a.h 1
8976.2.a.i 1
8976.2.a.j 1
8976.2.a.k 1
8976.2.a.l 1
8976.2.a.m 1
8976.2.a.n 1
8976.2.a.o 1
8976.2.a.p 1
8976.2.a.q 1
8976.2.a.r 1
8976.2.a.s 1
8976.2.a.t 1
8976.2.a.u 1
8976.2.a.v 1
8976.2.a.w 1
8976.2.a.x 1
8976.2.a.y 1
8976.2.a.z 1
8976.2.a.ba 1
8976.2.a.bb 1
8976.2.a.bc 1
8976.2.a.bd 1
8976.2.a.be 1
8976.2.a.bf 1
8976.2.a.bg 2
8976.2.a.bh 2
8976.2.a.bi 2
8976.2.a.bj 2
8976.2.a.bk 2
8976.2.a.bl 2
8976.2.a.bm 2
8976.2.a.bn 2
8976.2.a.bo 2
8976.2.a.bp 2
8976.2.a.bq 2
8976.2.a.br 2
8976.2.a.bs 2
8976.2.a.bt 3
8976.2.a.bu 3
8976.2.a.bv 3
8976.2.a.bw 3
8976.2.a.bx 3
8976.2.a.by 3
8976.2.a.bz 3
8976.2.a.ca 3
8976.2.a.cb 3
8976.2.a.cc 3
8976.2.a.cd 4
8976.2.a.ce 4
8976.2.a.cf 4
8976.2.a.cg 4
8976.2.a.ch 5
8976.2.a.ci 5
8976.2.a.cj 5
8976.2.a.ck 5
8976.2.a.cl 5
8976.2.a.cm 6
8976.2.a.cn 6
8976.2.a.co 6
8976.2.a.cp 6
8976.2.a.cq 7
8976.2.b \(\chi_{8976}(2177, \cdot)\) n/a 384 1
8976.2.e \(\chi_{8976}(5983, \cdot)\) n/a 216 1
8976.2.g \(\chi_{8976}(1871, \cdot)\) n/a 320 1
8976.2.h \(\chi_{8976}(7921, \cdot)\) n/a 180 1
8976.2.k \(\chi_{8976}(4489, \cdot)\) None 0 1
8976.2.l \(\chi_{8976}(5303, \cdot)\) None 0 1
8976.2.n \(\chi_{8976}(2551, \cdot)\) None 0 1
8976.2.q \(\chi_{8976}(5609, \cdot)\) None 0 1
8976.2.r \(\chi_{8976}(3433, \cdot)\) None 0 1
8976.2.u \(\chi_{8976}(6359, \cdot)\) None 0 1
8976.2.w \(\chi_{8976}(1495, \cdot)\) None 0 1
8976.2.x \(\chi_{8976}(6665, \cdot)\) None 0 1
8976.2.ba \(\chi_{8976}(1121, \cdot)\) n/a 428 1
8976.2.bb \(\chi_{8976}(7039, \cdot)\) n/a 192 1
8976.2.bd \(\chi_{8976}(815, \cdot)\) n/a 360 1
8976.2.bg \(\chi_{8976}(1891, \cdot)\) n/a 1728 2
8976.2.bi \(\chi_{8976}(6005, \cdot)\) n/a 3440 2
8976.2.bl \(\chi_{8976}(8317, \cdot)\) n/a 1440 2
8976.2.bn \(\chi_{8976}(1211, \cdot)\) n/a 2880 2
8976.2.bp \(\chi_{8976}(3365, \cdot)\) n/a 3440 2
8976.2.bq \(\chi_{8976}(2245, \cdot)\) n/a 1280 2
8976.2.bt \(\chi_{8976}(307, \cdot)\) n/a 1536 2
8976.2.bu \(\chi_{8976}(3059, \cdot)\) n/a 2880 2
8976.2.bw \(\chi_{8976}(3719, \cdot)\) None 0 2
8976.2.by \(\chi_{8976}(4399, \cdot)\) n/a 432 2
8976.2.cb \(\chi_{8976}(1849, \cdot)\) None 0 2
8976.2.cd \(\chi_{8976}(3761, \cdot)\) n/a 856 2
8976.2.ce \(\chi_{8976}(4025, \cdot)\) None 0 2
8976.2.cg \(\chi_{8976}(1585, \cdot)\) n/a 360 2
8976.2.cj \(\chi_{8976}(4135, \cdot)\) None 0 2
8976.2.cl \(\chi_{8976}(3455, \cdot)\) n/a 720 2
8976.2.cn \(\chi_{8976}(4115, \cdot)\) n/a 2560 2
8976.2.co \(\chi_{8976}(3739, \cdot)\) n/a 1728 2
8976.2.cr \(\chi_{8976}(1189, \cdot)\) n/a 1440 2
8976.2.cs \(\chi_{8976}(4421, \cdot)\) n/a 3072 2
8976.2.cv \(\chi_{8976}(5699, \cdot)\) n/a 2880 2
8976.2.cx \(\chi_{8976}(3829, \cdot)\) n/a 1440 2
8976.2.cy \(\chi_{8976}(1517, \cdot)\) n/a 3440 2
8976.2.da \(\chi_{8976}(6379, \cdot)\) n/a 1728 2
8976.2.dc \(\chi_{8976}(817, \cdot)\) n/a 768 4
8976.2.de \(\chi_{8976}(1385, \cdot)\) None 0 4
8976.2.df \(\chi_{8976}(967, \cdot)\) None 0 4
8976.2.di \(\chi_{8976}(287, \cdot)\) n/a 1440 4
8976.2.dj \(\chi_{8976}(529, \cdot)\) n/a 720 4
8976.2.dn \(\chi_{8976}(5149, \cdot)\) n/a 2880 4
8976.2.do \(\chi_{8976}(155, \cdot)\) n/a 5760 4
8976.2.dr \(\chi_{8976}(2837, \cdot)\) n/a 6880 4
8976.2.ds \(\chi_{8976}(43, \cdot)\) n/a 3456 4
8976.2.dt \(\chi_{8976}(2531, \cdot)\) n/a 5760 4
8976.2.du \(\chi_{8976}(661, \cdot)\) n/a 2880 4
8976.2.dx \(\chi_{8976}(3211, \cdot)\) n/a 3456 4
8976.2.dy \(\chi_{8976}(461, \cdot)\) n/a 6880 4
8976.2.eb \(\chi_{8976}(2905, \cdot)\) None 0 4
8976.2.ee \(\chi_{8976}(1079, \cdot)\) None 0 4
8976.2.ef \(\chi_{8976}(1759, \cdot)\) n/a 864 4
8976.2.ei \(\chi_{8976}(593, \cdot)\) n/a 1712 4
8976.2.ek \(\chi_{8976}(1631, \cdot)\) n/a 1728 4
8976.2.em \(\chi_{8976}(1327, \cdot)\) n/a 768 4
8976.2.ep \(\chi_{8976}(305, \cdot)\) n/a 1712 4
8976.2.eq \(\chi_{8976}(953, \cdot)\) None 0 4
8976.2.et \(\chi_{8976}(679, \cdot)\) None 0 4
8976.2.ev \(\chi_{8976}(647, \cdot)\) None 0 4
8976.2.ew \(\chi_{8976}(169, \cdot)\) None 0 4
8976.2.ez \(\chi_{8976}(2345, \cdot)\) None 0 4
8976.2.fa \(\chi_{8976}(919, \cdot)\) None 0 4
8976.2.fc \(\chi_{8976}(2039, \cdot)\) None 0 4
8976.2.ff \(\chi_{8976}(1225, \cdot)\) None 0 4
8976.2.fg \(\chi_{8976}(577, \cdot)\) n/a 864 4
8976.2.fj \(\chi_{8976}(2687, \cdot)\) n/a 1536 4
8976.2.fl \(\chi_{8976}(271, \cdot)\) n/a 864 4
8976.2.fm \(\chi_{8976}(545, \cdot)\) n/a 1536 4
8976.2.fp \(\chi_{8976}(1013, \cdot)\) n/a 11520 8
8976.2.fq \(\chi_{8976}(109, \cdot)\) n/a 6912 8
8976.2.ft \(\chi_{8976}(923, \cdot)\) n/a 13760 8
8976.2.fu \(\chi_{8976}(1387, \cdot)\) n/a 5760 8
8976.2.fy \(\chi_{8976}(881, \cdot)\) n/a 2880 8
8976.2.fz \(\chi_{8976}(241, \cdot)\) n/a 1728 8
8976.2.ga \(\chi_{8976}(2111, \cdot)\) n/a 3456 8
8976.2.gb \(\chi_{8976}(991, \cdot)\) n/a 1440 8
8976.2.gg \(\chi_{8976}(1319, \cdot)\) None 0 8
8976.2.gh \(\chi_{8976}(199, \cdot)\) None 0 8
8976.2.gi \(\chi_{8976}(617, \cdot)\) None 0 8
8976.2.gj \(\chi_{8976}(505, \cdot)\) None 0 8
8976.2.gm \(\chi_{8976}(2749, \cdot)\) n/a 6912 8
8976.2.gp \(\chi_{8976}(2069, \cdot)\) n/a 11520 8
8976.2.gq \(\chi_{8976}(2443, \cdot)\) n/a 5760 8
8976.2.gt \(\chi_{8976}(131, \cdot)\) n/a 13760 8
8976.2.gv \(\chi_{8976}(667, \cdot)\) n/a 6912 8
8976.2.gx \(\chi_{8976}(149, \cdot)\) n/a 13760 8
8976.2.gy \(\chi_{8976}(565, \cdot)\) n/a 6912 8
8976.2.ha \(\chi_{8976}(251, \cdot)\) n/a 13760 8
8976.2.hd \(\chi_{8976}(475, \cdot)\) n/a 6912 8
8976.2.he \(\chi_{8976}(443, \cdot)\) n/a 12288 8
8976.2.hh \(\chi_{8976}(1157, \cdot)\) n/a 12288 8
8976.2.hi \(\chi_{8976}(2005, \cdot)\) n/a 6912 8
8976.2.hk \(\chi_{8976}(47, \cdot)\) n/a 3456 8
8976.2.hm \(\chi_{8976}(871, \cdot)\) None 0 8
8976.2.hp \(\chi_{8976}(625, \cdot)\) n/a 1728 8
8976.2.hr \(\chi_{8976}(761, \cdot)\) None 0 8
8976.2.hs \(\chi_{8976}(497, \cdot)\) n/a 3424 8
8976.2.hu \(\chi_{8976}(361, \cdot)\) None 0 8
8976.2.hx \(\chi_{8976}(1135, \cdot)\) n/a 1728 8
8976.2.hz \(\chi_{8976}(455, \cdot)\) None 0 8
8976.2.ib \(\chi_{8976}(1021, \cdot)\) n/a 6144 8
8976.2.ic \(\chi_{8976}(101, \cdot)\) n/a 13760 8
8976.2.if \(\chi_{8976}(203, \cdot)\) n/a 13760 8
8976.2.ig \(\chi_{8976}(1531, \cdot)\) n/a 6144 8
8976.2.ii \(\chi_{8976}(2027, \cdot)\) n/a 13760 8
8976.2.ik \(\chi_{8976}(157, \cdot)\) n/a 6912 8
8976.2.in \(\chi_{8976}(293, \cdot)\) n/a 13760 8
8976.2.ip \(\chi_{8976}(259, \cdot)\) n/a 6912 8
8976.2.iq \(\chi_{8976}(127, \cdot)\) n/a 3456 16
8976.2.it \(\chi_{8976}(161, \cdot)\) n/a 6848 16
8976.2.iu \(\chi_{8976}(25, \cdot)\) None 0 16
8976.2.ix \(\chi_{8976}(1175, \cdot)\) None 0 16
8976.2.ja \(\chi_{8976}(1613, \cdot)\) n/a 27520 16
8976.2.jb \(\chi_{8976}(739, \cdot)\) n/a 13824 16
8976.2.je \(\chi_{8976}(1477, \cdot)\) n/a 13824 16
8976.2.jf \(\chi_{8976}(59, \cdot)\) n/a 27520 16
8976.2.jg \(\chi_{8976}(19, \cdot)\) n/a 13824 16
8976.2.jh \(\chi_{8976}(365, \cdot)\) n/a 27520 16
8976.2.jk \(\chi_{8976}(179, \cdot)\) n/a 27520 16
8976.2.jl \(\chi_{8976}(229, \cdot)\) n/a 13824 16
8976.2.jp \(\chi_{8976}(383, \cdot)\) n/a 6912 16
8976.2.jq \(\chi_{8976}(49, \cdot)\) n/a 3456 16
8976.2.jt \(\chi_{8976}(281, \cdot)\) None 0 16
8976.2.ju \(\chi_{8976}(151, \cdot)\) None 0 16
8976.2.jw \(\chi_{8976}(299, \cdot)\) n/a 55040 32
8976.2.jz \(\chi_{8976}(163, \cdot)\) n/a 27648 32
8976.2.ka \(\chi_{8976}(5, \cdot)\) n/a 55040 32
8976.2.kd \(\chi_{8976}(469, \cdot)\) n/a 27648 32
8976.2.ke \(\chi_{8976}(295, \cdot)\) None 0 32
8976.2.kf \(\chi_{8976}(167, \cdot)\) None 0 32
8976.2.kk \(\chi_{8976}(73, \cdot)\) None 0 32
8976.2.kl \(\chi_{8976}(377, \cdot)\) None 0 32
8976.2.km \(\chi_{8976}(193, \cdot)\) n/a 6912 32
8976.2.kn \(\chi_{8976}(113, \cdot)\) n/a 13696 32
8976.2.ks \(\chi_{8976}(31, \cdot)\) n/a 6912 32
8976.2.kt \(\chi_{8976}(95, \cdot)\) n/a 13824 32
8976.2.kv \(\chi_{8976}(91, \cdot)\) n/a 27648 32
8976.2.kw \(\chi_{8976}(107, \cdot)\) n/a 55040 32
8976.2.kz \(\chi_{8976}(61, \cdot)\) n/a 27648 32
8976.2.la \(\chi_{8976}(245, \cdot)\) n/a 55040 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8976))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8976)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(187))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(374))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(408))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(528))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(561))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(748))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(816))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1122))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1496))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2244))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2992))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4488))\)\(^{\oplus 2}\)