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Properties

Label 8784.2
Level 8784
Weight 2
Dimension 951278
Nonzero newspaces 140
Sturm bound 8570880

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Defining parameters

Level: \( N \) = \( 8784 = 2^{4} \cdot 3^{2} \cdot 61 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 140 \)
Sturm bound: \(8570880\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8784))\).

Total New Old
Modular forms 2156160 956056 1200104
Cusp forms 2129281 951278 1178003
Eisenstein series 26879 4778 22101

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8784))\)

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
8784.2.a \(\chi_{8784}(1, \cdot)\) 8784.2.a.a 1 1
8784.2.a.b 1
8784.2.a.c 1
8784.2.a.d 1
8784.2.a.e 1
8784.2.a.f 1
8784.2.a.g 1
8784.2.a.h 1
8784.2.a.i 1
8784.2.a.j 1
8784.2.a.k 1
8784.2.a.l 1
8784.2.a.m 1
8784.2.a.n 1
8784.2.a.o 1
8784.2.a.p 1
8784.2.a.q 1
8784.2.a.r 1
8784.2.a.s 1
8784.2.a.t 1
8784.2.a.u 1
8784.2.a.v 1
8784.2.a.w 1
8784.2.a.x 1
8784.2.a.y 1
8784.2.a.z 1
8784.2.a.ba 1
8784.2.a.bb 2
8784.2.a.bc 2
8784.2.a.bd 2
8784.2.a.be 2
8784.2.a.bf 2
8784.2.a.bg 2
8784.2.a.bh 2
8784.2.a.bi 2
8784.2.a.bj 2
8784.2.a.bk 3
8784.2.a.bl 3
8784.2.a.bm 3
8784.2.a.bn 3
8784.2.a.bo 3
8784.2.a.bp 3
8784.2.a.bq 3
8784.2.a.br 3
8784.2.a.bs 4
8784.2.a.bt 4
8784.2.a.bu 4
8784.2.a.bv 4
8784.2.a.bw 4
8784.2.a.bx 5
8784.2.a.by 6
8784.2.a.bz 6
8784.2.a.ca 6
8784.2.a.cb 6
8784.2.a.cc 6
8784.2.a.cd 8
8784.2.a.ce 9
8784.2.a.cf 9
8784.2.b \(\chi_{8784}(5977, \cdot)\) None 0 1
8784.2.d \(\chi_{8784}(7199, \cdot)\) n/a 120 1
8784.2.g \(\chi_{8784}(4393, \cdot)\) None 0 1
8784.2.i \(\chi_{8784}(8783, \cdot)\) n/a 124 1
8784.2.j \(\chi_{8784}(2807, \cdot)\) None 0 1
8784.2.l \(\chi_{8784}(1585, \cdot)\) n/a 154 1
8784.2.o \(\chi_{8784}(4391, \cdot)\) None 0 1
8784.2.q \(\chi_{8784}(2929, \cdot)\) n/a 720 2
8784.2.r \(\chi_{8784}(7489, \cdot)\) n/a 308 2
8784.2.s \(\chi_{8784}(2209, \cdot)\) n/a 740 2
8784.2.t \(\chi_{8784}(1633, \cdot)\) n/a 740 2
8784.2.v \(\chi_{8784}(233, \cdot)\) None 0 2
8784.2.x \(\chi_{8784}(4015, \cdot)\) n/a 310 2
8784.2.ba \(\chi_{8784}(2197, \cdot)\) n/a 1200 2
8784.2.bb \(\chi_{8784}(2195, \cdot)\) n/a 992 2
8784.2.bd \(\chi_{8784}(1963, \cdot)\) n/a 1236 2
8784.2.bf \(\chi_{8784}(2429, \cdot)\) n/a 992 2
8784.2.bg \(\chi_{8784}(2573, \cdot)\) n/a 992 2
8784.2.bi \(\chi_{8784}(1819, \cdot)\) n/a 1236 2
8784.2.bk \(\chi_{8784}(611, \cdot)\) n/a 960 2
8784.2.bl \(\chi_{8784}(3781, \cdot)\) n/a 1236 2
8784.2.bo \(\chi_{8784}(8407, \cdot)\) None 0 2
8784.2.bq \(\chi_{8784}(4625, \cdot)\) n/a 248 2
8784.2.bs \(\chi_{8784}(2449, \cdot)\) n/a 616 4
8784.2.bt \(\chi_{8784}(745, \cdot)\) None 0 2
8784.2.bv \(\chi_{8784}(3647, \cdot)\) n/a 744 2
8784.2.by \(\chi_{8784}(1417, \cdot)\) None 0 2
8784.2.ca \(\chi_{8784}(623, \cdot)\) n/a 744 2
8784.2.cc \(\chi_{8784}(5233, \cdot)\) n/a 740 2
8784.2.ce \(\chi_{8784}(4439, \cdot)\) None 0 2
8784.2.ch \(\chi_{8784}(1463, \cdot)\) None 0 2
8784.2.cj \(\chi_{8784}(5111, \cdot)\) None 0 2
8784.2.cm \(\chi_{8784}(2305, \cdot)\) n/a 308 2
8784.2.co \(\chi_{8784}(1511, \cdot)\) None 0 2
8784.2.cp \(\chi_{8784}(4513, \cdot)\) n/a 740 2
8784.2.cr \(\chi_{8784}(5735, \cdot)\) None 0 2
8784.2.cu \(\chi_{8784}(2183, \cdot)\) None 0 2
8784.2.cx \(\chi_{8784}(47, \cdot)\) n/a 744 2
8784.2.cz \(\chi_{8784}(841, \cdot)\) None 0 2
8784.2.da \(\chi_{8784}(719, \cdot)\) n/a 248 2
8784.2.dc \(\chi_{8784}(3097, \cdot)\) None 0 2
8784.2.df \(\chi_{8784}(2927, \cdot)\) n/a 744 2
8784.2.dh \(\chi_{8784}(1465, \cdot)\) None 0 2
8784.2.di \(\chi_{8784}(1343, \cdot)\) n/a 720 2
8784.2.dk \(\chi_{8784}(121, \cdot)\) None 0 2
8784.2.dn \(\chi_{8784}(5903, \cdot)\) n/a 248 2
8784.2.dp \(\chi_{8784}(6697, \cdot)\) None 0 2
8784.2.dq \(\chi_{8784}(4223, \cdot)\) n/a 744 2
8784.2.ds \(\chi_{8784}(169, \cdot)\) None 0 2
8784.2.du \(\chi_{8784}(2759, \cdot)\) None 0 2
8784.2.dy \(\chi_{8784}(5015, \cdot)\) None 0 2
8784.2.ea \(\chi_{8784}(5809, \cdot)\) n/a 740 2
8784.2.eb \(\chi_{8784}(1223, \cdot)\) None 0 4
8784.2.ef \(\chi_{8784}(935, \cdot)\) None 0 4
8784.2.eh \(\chi_{8784}(3457, \cdot)\) n/a 616 4
8784.2.ei \(\chi_{8784}(217, \cdot)\) None 0 4
8784.2.ek \(\chi_{8784}(1871, \cdot)\) n/a 496 4
8784.2.en \(\chi_{8784}(1369, \cdot)\) None 0 4
8784.2.ep \(\chi_{8784}(863, \cdot)\) n/a 496 4
8784.2.eq \(\chi_{8784}(761, \cdot)\) None 0 4
8784.2.es \(\chi_{8784}(223, \cdot)\) n/a 1488 4
8784.2.eu \(\chi_{8784}(1697, \cdot)\) n/a 1480 4
8784.2.ex \(\chi_{8784}(833, \cdot)\) n/a 1480 4
8784.2.ey \(\chi_{8784}(1313, \cdot)\) n/a 496 4
8784.2.fa \(\chi_{8784}(2551, \cdot)\) None 0 4
8784.2.fd \(\chi_{8784}(631, \cdot)\) None 0 4
8784.2.fe \(\chi_{8784}(151, \cdot)\) None 0 4
8784.2.fg \(\chi_{8784}(2027, \cdot)\) n/a 5936 4
8784.2.fh \(\chi_{8784}(13, \cdot)\) n/a 5936 4
8784.2.fk \(\chi_{8784}(853, \cdot)\) n/a 5936 4
8784.2.fl \(\chi_{8784}(2075, \cdot)\) n/a 5760 4
8784.2.fq \(\chi_{8784}(3707, \cdot)\) n/a 1984 4
8784.2.fr \(\chi_{8784}(1573, \cdot)\) n/a 5936 4
8784.2.fs \(\chi_{8784}(779, \cdot)\) n/a 5936 4
8784.2.ft \(\chi_{8784}(109, \cdot)\) n/a 2472 4
8784.2.fx \(\chi_{8784}(1493, \cdot)\) n/a 1984 4
8784.2.fz \(\chi_{8784}(2827, \cdot)\) n/a 2472 4
8784.2.ga \(\chi_{8784}(101, \cdot)\) n/a 5936 4
8784.2.gc \(\chi_{8784}(1435, \cdot)\) n/a 5936 4
8784.2.ge \(\chi_{8784}(499, \cdot)\) n/a 5936 4
8784.2.gg \(\chi_{8784}(1363, \cdot)\) n/a 5936 4
8784.2.gi \(\chi_{8784}(965, \cdot)\) n/a 5936 4
8784.2.gk \(\chi_{8784}(29, \cdot)\) n/a 5936 4
8784.2.gn \(\chi_{8784}(2419, \cdot)\) n/a 5936 4
8784.2.gp \(\chi_{8784}(1973, \cdot)\) n/a 5936 4
8784.2.gr \(\chi_{8784}(2045, \cdot)\) n/a 5936 4
8784.2.gt \(\chi_{8784}(1109, \cdot)\) n/a 5936 4
8784.2.gv \(\chi_{8784}(2347, \cdot)\) n/a 5936 4
8784.2.gx \(\chi_{8784}(355, \cdot)\) n/a 5936 4
8784.2.gy \(\chi_{8784}(883, \cdot)\) n/a 2472 4
8784.2.ha \(\chi_{8784}(3437, \cdot)\) n/a 1984 4
8784.2.he \(\chi_{8784}(901, \cdot)\) n/a 2472 4
8784.2.hf \(\chi_{8784}(563, \cdot)\) n/a 5936 4
8784.2.hg \(\chi_{8784}(2941, \cdot)\) n/a 5936 4
8784.2.hh \(\chi_{8784}(2915, \cdot)\) n/a 1984 4
8784.2.hm \(\chi_{8784}(731, \cdot)\) n/a 5936 4
8784.2.hn \(\chi_{8784}(733, \cdot)\) n/a 5760 4
8784.2.hq \(\chi_{8784}(2149, \cdot)\) n/a 5936 4
8784.2.hr \(\chi_{8784}(1355, \cdot)\) n/a 5936 4
8784.2.ht \(\chi_{8784}(703, \cdot)\) n/a 620 4
8784.2.hu \(\chi_{8784}(4543, \cdot)\) n/a 1488 4
8784.2.hx \(\chi_{8784}(1087, \cdot)\) n/a 1488 4
8784.2.hz \(\chi_{8784}(5225, \cdot)\) None 0 4
8784.2.ia \(\chi_{8784}(1241, \cdot)\) None 0 4
8784.2.id \(\chi_{8784}(3161, \cdot)\) None 0 4
8784.2.if \(\chi_{8784}(4615, \cdot)\) None 0 4
8784.2.ih \(\chi_{8784}(5153, \cdot)\) n/a 1480 4
8784.2.ii \(\chi_{8784}(1201, \cdot)\) n/a 2960 8
8784.2.ij \(\chi_{8784}(625, \cdot)\) n/a 2960 8
8784.2.ik \(\chi_{8784}(241, \cdot)\) n/a 2960 8
8784.2.il \(\chi_{8784}(1297, \cdot)\) n/a 1232 8
8784.2.in \(\chi_{8784}(343, \cdot)\) None 0 8
8784.2.ip \(\chi_{8784}(1745, \cdot)\) n/a 992 8
8784.2.is \(\chi_{8784}(613, \cdot)\) n/a 4944 8
8784.2.it \(\chi_{8784}(827, \cdot)\) n/a 3968 8
8784.2.iu \(\chi_{8784}(451, \cdot)\) n/a 4944 8
8784.2.iw \(\chi_{8784}(1853, \cdot)\) n/a 3968 8
8784.2.iz \(\chi_{8784}(53, \cdot)\) n/a 3968 8
8784.2.jb \(\chi_{8784}(1243, \cdot)\) n/a 4944 8
8784.2.jc \(\chi_{8784}(1979, \cdot)\) n/a 3968 8
8784.2.jd \(\chi_{8784}(253, \cdot)\) n/a 4944 8
8784.2.jg \(\chi_{8784}(89, \cdot)\) None 0 8
8784.2.ji \(\chi_{8784}(1135, \cdot)\) n/a 1240 8
8784.2.jk \(\chi_{8784}(1703, \cdot)\) None 0 8
8784.2.jm \(\chi_{8784}(49, \cdot)\) n/a 2960 8
8784.2.jp \(\chi_{8784}(839, \cdot)\) None 0 8
8784.2.js \(\chi_{8784}(527, \cdot)\) n/a 2976 8
8784.2.ju \(\chi_{8784}(25, \cdot)\) None 0 8
8784.2.jw \(\chi_{8784}(95, \cdot)\) n/a 2976 8
8784.2.jy \(\chi_{8784}(601, \cdot)\) None 0 8
8784.2.jz \(\chi_{8784}(2879, \cdot)\) n/a 992 8
8784.2.kb \(\chi_{8784}(649, \cdot)\) None 0 8
8784.2.ke \(\chi_{8784}(431, \cdot)\) n/a 992 8
8784.2.kg \(\chi_{8784}(73, \cdot)\) None 0 8
8784.2.kh \(\chi_{8784}(479, \cdot)\) n/a 2976 8
8784.2.kj \(\chi_{8784}(985, \cdot)\) None 0 8
8784.2.kl \(\chi_{8784}(239, \cdot)\) n/a 2976 8
8784.2.kn \(\chi_{8784}(2425, \cdot)\) None 0 8
8784.2.kr \(\chi_{8784}(167, \cdot)\) None 0 8
8784.2.ks \(\chi_{8784}(289, \cdot)\) n/a 1232 8
8784.2.ku \(\chi_{8784}(503, \cdot)\) None 0 8
8784.2.kx \(\chi_{8784}(529, \cdot)\) n/a 2960 8
8784.2.kz \(\chi_{8784}(119, \cdot)\) None 0 8
8784.2.lb \(\chi_{8784}(407, \cdot)\) None 0 8
8784.2.lf \(\chi_{8784}(3095, \cdot)\) None 0 8
8784.2.lg \(\chi_{8784}(97, \cdot)\) n/a 2960 8
8784.2.li \(\chi_{8784}(1175, \cdot)\) None 0 8
8784.2.lk \(\chi_{8784}(553, \cdot)\) None 0 8
8784.2.lm \(\chi_{8784}(2543, \cdot)\) n/a 2976 8
8784.2.lp \(\chi_{8784}(2761, \cdot)\) None 0 8
8784.2.lr \(\chi_{8784}(1391, \cdot)\) n/a 2976 8
8784.2.ls \(\chi_{8784}(7, \cdot)\) None 0 16
8784.2.lu \(\chi_{8784}(401, \cdot)\) n/a 5920 16
8784.2.lw \(\chi_{8784}(175, \cdot)\) n/a 5952 16
8784.2.lz \(\chi_{8784}(1039, \cdot)\) n/a 5952 16
8784.2.ma \(\chi_{8784}(559, \cdot)\) n/a 2480 16
8784.2.mc \(\chi_{8784}(281, \cdot)\) None 0 16
8784.2.mf \(\chi_{8784}(665, \cdot)\) None 0 16
8784.2.mg \(\chi_{8784}(185, \cdot)\) None 0 16
8784.2.mi \(\chi_{8784}(1811, \cdot)\) n/a 23744 16
8784.2.mj \(\chi_{8784}(229, \cdot)\) n/a 23744 16
8784.2.mm \(\chi_{8784}(949, \cdot)\) n/a 23744 16
8784.2.mn \(\chi_{8784}(491, \cdot)\) n/a 23744 16
8784.2.ms \(\chi_{8784}(107, \cdot)\) n/a 7936 16
8784.2.mt \(\chi_{8784}(205, \cdot)\) n/a 23744 16
8784.2.mu \(\chi_{8784}(371, \cdot)\) n/a 23744 16
8784.2.mv \(\chi_{8784}(469, \cdot)\) n/a 9888 16
8784.2.my \(\chi_{8784}(701, \cdot)\) n/a 7936 16
8784.2.na \(\chi_{8784}(307, \cdot)\) n/a 9888 16
8784.2.nd \(\chi_{8784}(67, \cdot)\) n/a 23744 16
8784.2.nf \(\chi_{8784}(211, \cdot)\) n/a 23744 16
8784.2.nh \(\chi_{8784}(653, \cdot)\) n/a 23744 16
8784.2.nj \(\chi_{8784}(221, \cdot)\) n/a 23744 16
8784.2.nl \(\chi_{8784}(1373, \cdot)\) n/a 23744 16
8784.2.nn \(\chi_{8784}(115, \cdot)\) n/a 23744 16
8784.2.no \(\chi_{8784}(821, \cdot)\) n/a 23744 16
8784.2.nq \(\chi_{8784}(173, \cdot)\) n/a 23744 16
8784.2.ns \(\chi_{8784}(643, \cdot)\) n/a 23744 16
8784.2.nu \(\chi_{8784}(763, \cdot)\) n/a 23744 16
8784.2.nw \(\chi_{8784}(43, \cdot)\) n/a 23744 16
8784.2.ny \(\chi_{8784}(437, \cdot)\) n/a 23744 16
8784.2.ob \(\chi_{8784}(91, \cdot)\) n/a 9888 16
8784.2.od \(\chi_{8784}(917, \cdot)\) n/a 7936 16
8784.2.og \(\chi_{8784}(829, \cdot)\) n/a 9888 16
8784.2.oh \(\chi_{8784}(83, \cdot)\) n/a 23744 16
8784.2.oi \(\chi_{8784}(493, \cdot)\) n/a 23744 16
8784.2.oj \(\chi_{8784}(179, \cdot)\) n/a 7936 16
8784.2.oo \(\chi_{8784}(131, \cdot)\) n/a 23744 16
8784.2.op \(\chi_{8784}(637, \cdot)\) n/a 23744 16
8784.2.os \(\chi_{8784}(1093, \cdot)\) n/a 23744 16
8784.2.ot \(\chi_{8784}(659, \cdot)\) n/a 23744 16
8784.2.ov \(\chi_{8784}(17, \cdot)\) n/a 1984 16
8784.2.ow \(\chi_{8784}(209, \cdot)\) n/a 5920 16
8784.2.oz \(\chi_{8784}(785, \cdot)\) n/a 5920 16
8784.2.pb \(\chi_{8784}(295, \cdot)\) None 0 16
8784.2.pc \(\chi_{8784}(55, \cdot)\) None 0 16
8784.2.pf \(\chi_{8784}(679, \cdot)\) None 0 16
8784.2.ph \(\chi_{8784}(425, \cdot)\) None 0 16
8784.2.pj \(\chi_{8784}(31, \cdot)\) n/a 5952 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8784))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8784)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(61))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(122))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(183))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(244))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(366))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(488))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(549))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(732))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(976))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1098))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1464))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2196))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2928))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8784))\)\(^{\oplus 1}\)