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Properties

Label 8325.2
Level 8325
Weight 2
Dimension 1787613
Nonzero newspaces 160
Sturm bound 9849600

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Defining parameters

Level: \( N \) = \( 8325 = 3^{2} \cdot 5^{2} \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 160 \)
Sturm bound: \(9849600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8325))\).

Total New Old
Modular forms 2478528 1800527 678001
Cusp forms 2446273 1787613 658660
Eisenstein series 32255 12914 19341

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8325))\)

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
8325.2.a \(\chi_{8325}(1, \cdot)\) 8325.2.a.a 1 1
8325.2.a.b 1
8325.2.a.c 1
8325.2.a.d 1
8325.2.a.e 1
8325.2.a.f 1
8325.2.a.g 1
8325.2.a.h 1
8325.2.a.i 1
8325.2.a.j 1
8325.2.a.k 1
8325.2.a.l 1
8325.2.a.m 1
8325.2.a.n 1
8325.2.a.o 1
8325.2.a.p 1
8325.2.a.q 1
8325.2.a.r 1
8325.2.a.s 1
8325.2.a.t 1
8325.2.a.u 1
8325.2.a.v 1
8325.2.a.w 1
8325.2.a.x 1
8325.2.a.y 1
8325.2.a.z 1
8325.2.a.ba 1
8325.2.a.bb 1
8325.2.a.bc 1
8325.2.a.bd 1
8325.2.a.be 1
8325.2.a.bf 2
8325.2.a.bg 2
8325.2.a.bh 2
8325.2.a.bi 2
8325.2.a.bj 2
8325.2.a.bk 2
8325.2.a.bl 2
8325.2.a.bm 2
8325.2.a.bn 2
8325.2.a.bo 3
8325.2.a.bp 3
8325.2.a.bq 3
8325.2.a.br 3
8325.2.a.bs 3
8325.2.a.bt 4
8325.2.a.bu 4
8325.2.a.bv 4
8325.2.a.bw 4
8325.2.a.bx 5
8325.2.a.by 5
8325.2.a.bz 5
8325.2.a.ca 5
8325.2.a.cb 5
8325.2.a.cc 5
8325.2.a.cd 5
8325.2.a.ce 5
8325.2.a.cf 5
8325.2.a.cg 5
8325.2.a.ch 5
8325.2.a.ci 6
8325.2.a.cj 6
8325.2.a.ck 6
8325.2.a.cl 6
8325.2.a.cm 7
8325.2.a.cn 7
8325.2.a.co 8
8325.2.a.cp 8
8325.2.a.cq 9
8325.2.a.cr 9
8325.2.a.cs 10
8325.2.a.ct 10
8325.2.a.cu 13
8325.2.a.cv 13
8325.2.a.cw 16
8325.2.a.cx 16
8325.2.c \(\chi_{8325}(1999, \cdot)\) n/a 270 1
8325.2.e \(\chi_{8325}(5401, \cdot)\) n/a 298 1
8325.2.g \(\chi_{8325}(7399, \cdot)\) n/a 284 1
8325.2.i \(\chi_{8325}(2776, \cdot)\) n/a 1368 2
8325.2.j \(\chi_{8325}(676, \cdot)\) n/a 598 2
8325.2.k \(\chi_{8325}(1876, \cdot)\) n/a 1432 2
8325.2.l \(\chi_{8325}(3451, \cdot)\) n/a 1432 2
8325.2.m \(\chi_{8325}(2818, \cdot)\) n/a 566 2
8325.2.p \(\chi_{8325}(5174, \cdot)\) n/a 456 2
8325.2.q \(\chi_{8325}(332, \cdot)\) n/a 456 2
8325.2.r \(\chi_{8325}(593, \cdot)\) n/a 432 2
8325.2.v \(\chi_{8325}(3176, \cdot)\) n/a 484 2
8325.2.w \(\chi_{8325}(1918, \cdot)\) n/a 566 2
8325.2.y \(\chi_{8325}(1666, \cdot)\) n/a 1800 4
8325.2.z \(\chi_{8325}(3526, \cdot)\) n/a 1432 2
8325.2.bb \(\chi_{8325}(5449, \cdot)\) n/a 1360 2
8325.2.bd \(\chi_{8325}(2749, \cdot)\) n/a 1360 2
8325.2.bi \(\chi_{8325}(1849, \cdot)\) n/a 1360 2
8325.2.bk \(\chi_{8325}(6724, \cdot)\) n/a 568 2
8325.2.bm \(\chi_{8325}(3874, \cdot)\) n/a 1360 2
8325.2.bp \(\chi_{8325}(2626, \cdot)\) n/a 1432 2
8325.2.br \(\chi_{8325}(4726, \cdot)\) n/a 596 2
8325.2.bt \(\chi_{8325}(4774, \cdot)\) n/a 1296 2
8325.2.bv \(\chi_{8325}(1099, \cdot)\) n/a 564 2
8325.2.bw \(\chi_{8325}(751, \cdot)\) n/a 1432 2
8325.2.bz \(\chi_{8325}(1174, \cdot)\) n/a 1360 2
8325.2.cb \(\chi_{8325}(2401, \cdot)\) n/a 4296 6
8325.2.cc \(\chi_{8325}(451, \cdot)\) n/a 1788 6
8325.2.cd \(\chi_{8325}(601, \cdot)\) n/a 4296 6
8325.2.ce \(\chi_{8325}(739, \cdot)\) n/a 1888 4
8325.2.ch \(\chi_{8325}(334, \cdot)\) n/a 1800 4
8325.2.cj \(\chi_{8325}(406, \cdot)\) n/a 1896 4
8325.2.cm \(\chi_{8325}(1318, \cdot)\) n/a 2720 4
8325.2.cn \(\chi_{8325}(82, \cdot)\) n/a 1132 4
8325.2.cq \(\chi_{8325}(2707, \cdot)\) n/a 2720 4
8325.2.cr \(\chi_{8325}(1768, \cdot)\) n/a 2720 4
8325.2.ct \(\chi_{8325}(1451, \cdot)\) n/a 2864 4
8325.2.cx \(\chi_{8325}(1157, \cdot)\) n/a 2720 4
8325.2.cy \(\chi_{8325}(1343, \cdot)\) n/a 2720 4
8325.2.cz \(\chi_{8325}(3449, \cdot)\) n/a 2720 4
8325.2.db \(\chi_{8325}(3899, \cdot)\) n/a 2720 4
8325.2.de \(\chi_{8325}(401, \cdot)\) n/a 2864 4
8325.2.dg \(\chi_{8325}(251, \cdot)\) n/a 968 4
8325.2.dh \(\chi_{8325}(1232, \cdot)\) n/a 912 4
8325.2.di \(\chi_{8325}(1268, \cdot)\) n/a 912 4
8325.2.dn \(\chi_{8325}(482, \cdot)\) n/a 2592 4
8325.2.do \(\chi_{8325}(4043, \cdot)\) n/a 2720 4
8325.2.dp \(\chi_{8325}(2432, \cdot)\) n/a 2720 4
8325.2.dq \(\chi_{8325}(443, \cdot)\) n/a 2720 4
8325.2.du \(\chi_{8325}(524, \cdot)\) n/a 2720 4
8325.2.dw \(\chi_{8325}(674, \cdot)\) n/a 912 4
8325.2.dx \(\chi_{8325}(1901, \cdot)\) n/a 2864 4
8325.2.dz \(\chi_{8325}(532, \cdot)\) n/a 1132 4
8325.2.ec \(\chi_{8325}(193, \cdot)\) n/a 2720 4
8325.2.ed \(\chi_{8325}(43, \cdot)\) n/a 2720 4
8325.2.eg \(\chi_{8325}(643, \cdot)\) n/a 2720 4
8325.2.eh \(\chi_{8325}(121, \cdot)\) n/a 9088 8
8325.2.ei \(\chi_{8325}(766, \cdot)\) n/a 3776 8
8325.2.ej \(\chi_{8325}(556, \cdot)\) n/a 8640 8
8325.2.ek \(\chi_{8325}(211, \cdot)\) n/a 9088 8
8325.2.en \(\chi_{8325}(2224, \cdot)\) n/a 1704 6
8325.2.eo \(\chi_{8325}(724, \cdot)\) n/a 4080 6
8325.2.et \(\chi_{8325}(1024, \cdot)\) n/a 4080 6
8325.2.ew \(\chi_{8325}(49, \cdot)\) n/a 4080 6
8325.2.ex \(\chi_{8325}(2449, \cdot)\) n/a 1692 6
8325.2.ey \(\chi_{8325}(226, \cdot)\) n/a 1782 6
8325.2.ez \(\chi_{8325}(151, \cdot)\) n/a 4296 6
8325.2.fe \(\chi_{8325}(1501, \cdot)\) n/a 4296 6
8325.2.ff \(\chi_{8325}(349, \cdot)\) n/a 4080 6
8325.2.fh \(\chi_{8325}(253, \cdot)\) n/a 3784 8
8325.2.fi \(\chi_{8325}(179, \cdot)\) n/a 3040 8
8325.2.fm \(\chi_{8325}(1592, \cdot)\) n/a 2880 8
8325.2.fn \(\chi_{8325}(998, \cdot)\) n/a 3040 8
8325.2.fo \(\chi_{8325}(746, \cdot)\) n/a 3040 8
8325.2.fr \(\chi_{8325}(1153, \cdot)\) n/a 3784 8
8325.2.fu \(\chi_{8325}(529, \cdot)\) n/a 9088 8
8325.2.fw \(\chi_{8325}(544, \cdot)\) n/a 9088 8
8325.2.fx \(\chi_{8325}(1306, \cdot)\) n/a 3792 8
8325.2.fz \(\chi_{8325}(961, \cdot)\) n/a 9088 8
8325.2.gb \(\chi_{8325}(1009, \cdot)\) n/a 3792 8
8325.2.gd \(\chi_{8325}(889, \cdot)\) n/a 8640 8
8325.2.gg \(\chi_{8325}(286, \cdot)\) n/a 9088 8
8325.2.gi \(\chi_{8325}(619, \cdot)\) n/a 9088 8
8325.2.gl \(\chi_{8325}(64, \cdot)\) n/a 3776 8
8325.2.gn \(\chi_{8325}(184, \cdot)\) n/a 9088 8
8325.2.gr \(\chi_{8325}(196, \cdot)\) n/a 9088 8
8325.2.gt \(\chi_{8325}(454, \cdot)\) n/a 9088 8
8325.2.gu \(\chi_{8325}(718, \cdot)\) n/a 8160 12
8325.2.gx \(\chi_{8325}(457, \cdot)\) n/a 8160 12
8325.2.gy \(\chi_{8325}(757, \cdot)\) n/a 3396 12
8325.2.ha \(\chi_{8325}(707, \cdot)\) n/a 8160 12
8325.2.hd \(\chi_{8325}(293, \cdot)\) n/a 8160 12
8325.2.hg \(\chi_{8325}(476, \cdot)\) n/a 2880 12
8325.2.hh \(\chi_{8325}(1424, \cdot)\) n/a 8160 12
8325.2.hi \(\chi_{8325}(1226, \cdot)\) n/a 8592 12
8325.2.hj \(\chi_{8325}(224, \cdot)\) n/a 2736 12
8325.2.hm \(\chi_{8325}(182, \cdot)\) n/a 8160 12
8325.2.hn \(\chi_{8325}(107, \cdot)\) n/a 2736 12
8325.2.hs \(\chi_{8325}(818, \cdot)\) n/a 2736 12
8325.2.ht \(\chi_{8325}(632, \cdot)\) n/a 8160 12
8325.2.hv \(\chi_{8325}(1049, \cdot)\) n/a 8160 12
8325.2.hw \(\chi_{8325}(1001, \cdot)\) n/a 8592 12
8325.2.hy \(\chi_{8325}(832, \cdot)\) n/a 8160 12
8325.2.ib \(\chi_{8325}(568, \cdot)\) n/a 3396 12
8325.2.ic \(\chi_{8325}(607, \cdot)\) n/a 8160 12
8325.2.ie \(\chi_{8325}(16, \cdot)\) n/a 27264 24
8325.2.if \(\chi_{8325}(46, \cdot)\) n/a 11328 24
8325.2.ig \(\chi_{8325}(571, \cdot)\) n/a 27264 24
8325.2.ih \(\chi_{8325}(637, \cdot)\) n/a 18176 16
8325.2.ik \(\chi_{8325}(142, \cdot)\) n/a 18176 16
8325.2.il \(\chi_{8325}(763, \cdot)\) n/a 18176 16
8325.2.io \(\chi_{8325}(208, \cdot)\) n/a 7568 16
8325.2.iq \(\chi_{8325}(569, \cdot)\) n/a 18176 16
8325.2.ir \(\chi_{8325}(341, \cdot)\) n/a 6080 16
8325.2.it \(\chi_{8325}(191, \cdot)\) n/a 18176 16
8325.2.ix \(\chi_{8325}(887, \cdot)\) n/a 18176 16
8325.2.iy \(\chi_{8325}(122, \cdot)\) n/a 18176 16
8325.2.iz \(\chi_{8325}(47, \cdot)\) n/a 18176 16
8325.2.ja \(\chi_{8325}(38, \cdot)\) n/a 17280 16
8325.2.jf \(\chi_{8325}(602, \cdot)\) n/a 6080 16
8325.2.jg \(\chi_{8325}(233, \cdot)\) n/a 6080 16
8325.2.jh \(\chi_{8325}(134, \cdot)\) n/a 6080 16
8325.2.jj \(\chi_{8325}(734, \cdot)\) n/a 18176 16
8325.2.jm \(\chi_{8325}(236, \cdot)\) n/a 18176 16
8325.2.jo \(\chi_{8325}(356, \cdot)\) n/a 18176 16
8325.2.jp \(\chi_{8325}(212, \cdot)\) n/a 18176 16
8325.2.jq \(\chi_{8325}(137, \cdot)\) n/a 18176 16
8325.2.ju \(\chi_{8325}(14, \cdot)\) n/a 18176 16
8325.2.jw \(\chi_{8325}(88, \cdot)\) n/a 18176 16
8325.2.jx \(\chi_{8325}(808, \cdot)\) n/a 18176 16
8325.2.ka \(\chi_{8325}(658, \cdot)\) n/a 7568 16
8325.2.kb \(\chi_{8325}(547, \cdot)\) n/a 18176 16
8325.2.kd \(\chi_{8325}(229, \cdot)\) n/a 27264 24
8325.2.ke \(\chi_{8325}(691, \cdot)\) n/a 27264 24
8325.2.kj \(\chi_{8325}(391, \cdot)\) n/a 27264 24
8325.2.kk \(\chi_{8325}(136, \cdot)\) n/a 11376 24
8325.2.kl \(\chi_{8325}(379, \cdot)\) n/a 11376 24
8325.2.km \(\chi_{8325}(34, \cdot)\) n/a 27264 24
8325.2.kp \(\chi_{8325}(4, \cdot)\) n/a 27264 24
8325.2.ku \(\chi_{8325}(139, \cdot)\) n/a 27264 24
8325.2.kv \(\chi_{8325}(289, \cdot)\) n/a 11328 24
8325.2.kz \(\chi_{8325}(172, \cdot)\) n/a 22704 48
8325.2.la \(\chi_{8325}(277, \cdot)\) n/a 54528 48
8325.2.ld \(\chi_{8325}(13, \cdot)\) n/a 54528 48
8325.2.lf \(\chi_{8325}(146, \cdot)\) n/a 54528 48
8325.2.lg \(\chi_{8325}(479, \cdot)\) n/a 54528 48
8325.2.li \(\chi_{8325}(263, \cdot)\) n/a 54528 48
8325.2.lj \(\chi_{8325}(62, \cdot)\) n/a 18240 48
8325.2.lo \(\chi_{8325}(53, \cdot)\) n/a 18240 48
8325.2.lp \(\chi_{8325}(488, \cdot)\) n/a 54528 48
8325.2.ls \(\chi_{8325}(89, \cdot)\) n/a 18240 48
8325.2.lt \(\chi_{8325}(56, \cdot)\) n/a 54528 48
8325.2.lu \(\chi_{8325}(59, \cdot)\) n/a 54528 48
8325.2.lv \(\chi_{8325}(116, \cdot)\) n/a 18240 48
8325.2.ly \(\chi_{8325}(83, \cdot)\) n/a 54528 48
8325.2.mb \(\chi_{8325}(77, \cdot)\) n/a 54528 48
8325.2.md \(\chi_{8325}(22, \cdot)\) n/a 54528 48
8325.2.me \(\chi_{8325}(163, \cdot)\) n/a 22704 48
8325.2.mh \(\chi_{8325}(283, \cdot)\) n/a 54528 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8325))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8325)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(333))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(555))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(925))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1665))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2775))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8325))\)\(^{\oplus 1}\)