Properties

Label 9280.2
Level 9280
Weight 2
Dimension 1323828
Nonzero newspaces 104
Sturm bound 10321920

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Defining parameters

Level: \( N \) = \( 9280 = 2^{6} \cdot 5 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 104 \)
Sturm bound: \(10321920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9280))\).

Total New Old
Modular forms 2596608 1330956 1265652
Cusp forms 2564353 1323828 1240525
Eisenstein series 32255 7128 25127

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9280))\)

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
9280.2.a \(\chi_{9280}(1, \cdot)\) 9280.2.a.a 1 1
9280.2.a.b 1
9280.2.a.c 1
9280.2.a.d 1
9280.2.a.e 1
9280.2.a.f 1
9280.2.a.g 1
9280.2.a.h 1
9280.2.a.i 1
9280.2.a.j 1
9280.2.a.k 1
9280.2.a.l 1
9280.2.a.m 1
9280.2.a.n 1
9280.2.a.o 1
9280.2.a.p 1
9280.2.a.q 1
9280.2.a.r 1
9280.2.a.s 1
9280.2.a.t 1
9280.2.a.u 1
9280.2.a.v 1
9280.2.a.w 2
9280.2.a.x 2
9280.2.a.y 2
9280.2.a.z 2
9280.2.a.ba 2
9280.2.a.bb 2
9280.2.a.bc 2
9280.2.a.bd 2
9280.2.a.be 2
9280.2.a.bf 3
9280.2.a.bg 3
9280.2.a.bh 3
9280.2.a.bi 3
9280.2.a.bj 3
9280.2.a.bk 3
9280.2.a.bl 3
9280.2.a.bm 3
9280.2.a.bn 3
9280.2.a.bo 3
9280.2.a.bp 3
9280.2.a.bq 3
9280.2.a.br 3
9280.2.a.bs 3
9280.2.a.bt 3
9280.2.a.bu 3
9280.2.a.bv 3
9280.2.a.bw 3
9280.2.a.bx 3
9280.2.a.by 3
9280.2.a.bz 4
9280.2.a.ca 4
9280.2.a.cb 4
9280.2.a.cc 4
9280.2.a.cd 4
9280.2.a.ce 4
9280.2.a.cf 4
9280.2.a.cg 5
9280.2.a.ch 5
9280.2.a.ci 5
9280.2.a.cj 5
9280.2.a.ck 5
9280.2.a.cl 5
9280.2.a.cm 6
9280.2.a.cn 6
9280.2.a.co 6
9280.2.a.cp 6
9280.2.a.cq 7
9280.2.a.cr 7
9280.2.a.cs 8
9280.2.a.ct 10
9280.2.a.cu 10
9280.2.d \(\chi_{9280}(5569, \cdot)\) n/a 336 1
9280.2.e \(\chi_{9280}(289, \cdot)\) n/a 360 1
9280.2.f \(\chi_{9280}(4641, \cdot)\) n/a 224 1
9280.2.g \(\chi_{9280}(8641, \cdot)\) n/a 240 1
9280.2.j \(\chi_{9280}(4929, \cdot)\) n/a 356 1
9280.2.k \(\chi_{9280}(929, \cdot)\) n/a 336 1
9280.2.p \(\chi_{9280}(4001, \cdot)\) n/a 240 1
9280.2.q \(\chi_{9280}(1839, \cdot)\) n/a 712 2
9280.2.t \(\chi_{9280}(5103, \cdot)\) n/a 712 2
9280.2.u \(\chi_{9280}(737, \cdot)\) n/a 720 2
9280.2.w \(\chi_{9280}(6977, \cdot)\) n/a 712 2
9280.2.z \(\chi_{9280}(1103, \cdot)\) n/a 672 2
9280.2.bb \(\chi_{9280}(911, \cdot)\) n/a 480 2
9280.2.bc \(\chi_{9280}(191, \cdot)\) n/a 480 2
9280.2.bf \(\chi_{9280}(1681, \cdot)\) n/a 480 2
9280.2.bh \(\chi_{9280}(2321, \cdot)\) n/a 448 2
9280.2.bi \(\chi_{9280}(3231, \cdot)\) n/a 480 2
9280.2.bl \(\chi_{9280}(17, \cdot)\) n/a 712 2
9280.2.bo \(\chi_{9280}(6207, \cdot)\) n/a 672 2
9280.2.bp \(\chi_{9280}(927, \cdot)\) n/a 720 2
9280.2.bq \(\chi_{9280}(1873, \cdot)\) n/a 712 2
9280.2.bs \(\chi_{9280}(6513, \cdot)\) n/a 712 2
9280.2.bu \(\chi_{9280}(1567, \cdot)\) n/a 672 2
9280.2.bv \(\chi_{9280}(5567, \cdot)\) n/a 712 2
9280.2.bz \(\chi_{9280}(273, \cdot)\) n/a 712 2
9280.2.cb \(\chi_{9280}(1119, \cdot)\) n/a 720 2
9280.2.cc \(\chi_{9280}(3249, \cdot)\) n/a 672 2
9280.2.ce \(\chi_{9280}(2609, \cdot)\) n/a 712 2
9280.2.ch \(\chi_{9280}(4159, \cdot)\) n/a 712 2
9280.2.cj \(\chi_{9280}(3439, \cdot)\) n/a 712 2
9280.2.ck \(\chi_{9280}(5743, \cdot)\) n/a 672 2
9280.2.cn \(\chi_{9280}(5377, \cdot)\) n/a 712 2
9280.2.cp \(\chi_{9280}(2337, \cdot)\) n/a 720 2
9280.2.cq \(\chi_{9280}(463, \cdot)\) n/a 712 2
9280.2.cs \(\chi_{9280}(2511, \cdot)\) n/a 480 2
9280.2.cu \(\chi_{9280}(1921, \cdot)\) n/a 1440 6
9280.2.cw \(\chi_{9280}(1177, \cdot)\) None 0 4
9280.2.cy \(\chi_{9280}(407, \cdot)\) None 0 4
9280.2.da \(\chi_{9280}(3943, \cdot)\) None 0 4
9280.2.db \(\chi_{9280}(713, \cdot)\) None 0 4
9280.2.dd \(\chi_{9280}(1449, \cdot)\) None 0 4
9280.2.dg \(\chi_{9280}(1161, \cdot)\) None 0 4
9280.2.dh \(\chi_{9280}(3671, \cdot)\) None 0 4
9280.2.dk \(\chi_{9280}(1351, \cdot)\) None 0 4
9280.2.dl \(\chi_{9280}(679, \cdot)\) None 0 4
9280.2.do \(\chi_{9280}(2279, \cdot)\) None 0 4
9280.2.dq \(\chi_{9280}(521, \cdot)\) None 0 4
9280.2.dr \(\chi_{9280}(2089, \cdot)\) None 0 4
9280.2.dt \(\chi_{9280}(1433, \cdot)\) None 0 4
9280.2.dv \(\chi_{9280}(2263, \cdot)\) None 0 4
9280.2.dx \(\chi_{9280}(1623, \cdot)\) None 0 4
9280.2.ea \(\chi_{9280}(1897, \cdot)\) None 0 4
9280.2.eb \(\chi_{9280}(2081, \cdot)\) n/a 1440 6
9280.2.eg \(\chi_{9280}(2849, \cdot)\) n/a 2160 6
9280.2.eh \(\chi_{9280}(129, \cdot)\) n/a 2136 6
9280.2.ek \(\chi_{9280}(961, \cdot)\) n/a 1440 6
9280.2.el \(\chi_{9280}(161, \cdot)\) n/a 1440 6
9280.2.em \(\chi_{9280}(1889, \cdot)\) n/a 2160 6
9280.2.en \(\chi_{9280}(1089, \cdot)\) n/a 2136 6
9280.2.er \(\chi_{9280}(347, \cdot)\) n/a 11488 8
9280.2.es \(\chi_{9280}(1259, \cdot)\) n/a 11488 8
9280.2.eu \(\chi_{9280}(1491, \cdot)\) n/a 7680 8
9280.2.ex \(\chi_{9280}(523, \cdot)\) n/a 10752 8
9280.2.ez \(\chi_{9280}(581, \cdot)\) n/a 7168 8
9280.2.fa \(\chi_{9280}(349, \cdot)\) n/a 10752 8
9280.2.fc \(\chi_{9280}(133, \cdot)\) n/a 11488 8
9280.2.ff \(\chi_{9280}(597, \cdot)\) n/a 11488 8
9280.2.fg \(\chi_{9280}(1293, \cdot)\) n/a 11488 8
9280.2.fj \(\chi_{9280}(853, \cdot)\) n/a 11488 8
9280.2.fl \(\chi_{9280}(1101, \cdot)\) n/a 7680 8
9280.2.fm \(\chi_{9280}(869, \cdot)\) n/a 11488 8
9280.2.fo \(\chi_{9280}(1507, \cdot)\) n/a 11488 8
9280.2.fr \(\chi_{9280}(99, \cdot)\) n/a 11488 8
9280.2.ft \(\chi_{9280}(331, \cdot)\) n/a 7680 8
9280.2.fu \(\chi_{9280}(987, \cdot)\) n/a 10752 8
9280.2.fx \(\chi_{9280}(591, \cdot)\) n/a 2880 12
9280.2.fz \(\chi_{9280}(1327, \cdot)\) n/a 4272 12
9280.2.ga \(\chi_{9280}(193, \cdot)\) n/a 4272 12
9280.2.gc \(\chi_{9280}(417, \cdot)\) n/a 4320 12
9280.2.gf \(\chi_{9280}(1167, \cdot)\) n/a 4272 12
9280.2.gg \(\chi_{9280}(1519, \cdot)\) n/a 4272 12
9280.2.gi \(\chi_{9280}(959, \cdot)\) n/a 4272 12
9280.2.gl \(\chi_{9280}(49, \cdot)\) n/a 4272 12
9280.2.gn \(\chi_{9280}(209, \cdot)\) n/a 4272 12
9280.2.go \(\chi_{9280}(159, \cdot)\) n/a 4320 12
9280.2.gr \(\chi_{9280}(177, \cdot)\) n/a 4272 12
9280.2.gu \(\chi_{9280}(63, \cdot)\) n/a 4272 12
9280.2.gv \(\chi_{9280}(223, \cdot)\) n/a 4320 12
9280.2.gw \(\chi_{9280}(337, \cdot)\) n/a 4272 12
9280.2.gy \(\chi_{9280}(913, \cdot)\) n/a 4272 12
9280.2.ha \(\chi_{9280}(863, \cdot)\) n/a 4320 12
9280.2.hb \(\chi_{9280}(703, \cdot)\) n/a 4272 12
9280.2.hf \(\chi_{9280}(113, \cdot)\) n/a 4272 12
9280.2.hh \(\chi_{9280}(31, \cdot)\) n/a 2880 12
9280.2.hi \(\chi_{9280}(241, \cdot)\) n/a 2880 12
9280.2.hk \(\chi_{9280}(81, \cdot)\) n/a 2880 12
9280.2.hn \(\chi_{9280}(511, \cdot)\) n/a 2880 12
9280.2.ho \(\chi_{9280}(271, \cdot)\) n/a 2880 12
9280.2.hq \(\chi_{9280}(687, \cdot)\) n/a 4272 12
9280.2.ht \(\chi_{9280}(97, \cdot)\) n/a 4320 12
9280.2.hv \(\chi_{9280}(2177, \cdot)\) n/a 4272 12
9280.2.hw \(\chi_{9280}(207, \cdot)\) n/a 4272 12
9280.2.hz \(\chi_{9280}(79, \cdot)\) n/a 4272 12
9280.2.ia \(\chi_{9280}(137, \cdot)\) None 0 24
9280.2.ic \(\chi_{9280}(167, \cdot)\) None 0 24
9280.2.ie \(\chi_{9280}(7, \cdot)\) None 0 24
9280.2.ih \(\chi_{9280}(617, \cdot)\) None 0 24
9280.2.ii \(\chi_{9280}(281, \cdot)\) None 0 24
9280.2.il \(\chi_{9280}(9, \cdot)\) None 0 24
9280.2.in \(\chi_{9280}(279, \cdot)\) None 0 24
9280.2.io \(\chi_{9280}(39, \cdot)\) None 0 24
9280.2.ir \(\chi_{9280}(391, \cdot)\) None 0 24
9280.2.is \(\chi_{9280}(311, \cdot)\) None 0 24
9280.2.iv \(\chi_{9280}(169, \cdot)\) None 0 24
9280.2.iw \(\chi_{9280}(121, \cdot)\) None 0 24
9280.2.iz \(\chi_{9280}(73, \cdot)\) None 0 24
9280.2.jb \(\chi_{9280}(903, \cdot)\) None 0 24
9280.2.jd \(\chi_{9280}(103, \cdot)\) None 0 24
9280.2.je \(\chi_{9280}(537, \cdot)\) None 0 24
9280.2.jg \(\chi_{9280}(123, \cdot)\) n/a 68928 48
9280.2.jj \(\chi_{9280}(11, \cdot)\) n/a 46080 48
9280.2.jl \(\chi_{9280}(19, \cdot)\) n/a 68928 48
9280.2.jm \(\chi_{9280}(187, \cdot)\) n/a 68928 48
9280.2.jp \(\chi_{9280}(109, \cdot)\) n/a 68928 48
9280.2.jq \(\chi_{9280}(341, \cdot)\) n/a 46080 48
9280.2.js \(\chi_{9280}(77, \cdot)\) n/a 68928 48
9280.2.jv \(\chi_{9280}(37, \cdot)\) n/a 68928 48
9280.2.jw \(\chi_{9280}(437, \cdot)\) n/a 68928 48
9280.2.jz \(\chi_{9280}(293, \cdot)\) n/a 68928 48
9280.2.kb \(\chi_{9280}(429, \cdot)\) n/a 68928 48
9280.2.kc \(\chi_{9280}(141, \cdot)\) n/a 46080 48
9280.2.kf \(\chi_{9280}(83, \cdot)\) n/a 68928 48
9280.2.kg \(\chi_{9280}(171, \cdot)\) n/a 46080 48
9280.2.ki \(\chi_{9280}(259, \cdot)\) n/a 68928 48
9280.2.kl \(\chi_{9280}(67, \cdot)\) n/a 68928 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9280))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9280)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(290))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(464))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(580))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(928))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1856))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2320))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4640))\)\(^{\oplus 2}\)