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Properties

Label 9350.2
Level 9350
Weight 2
Dimension 777614
Nonzero newspaces 126
Sturm bound 10368000

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Defining parameters

Level: \( N \) = \( 9350 = 2 \cdot 5^{2} \cdot 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 126 \)
Sturm bound: \(10368000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9350))\).

Total New Old
Modular forms 2609920 777614 1832306
Cusp forms 2574081 777614 1796467
Eisenstein series 35839 0 35839

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9350))\)

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
9350.2.a \(\chi_{9350}(1, \cdot)\) 9350.2.a.a 1 1
9350.2.a.b 1
9350.2.a.c 1
9350.2.a.d 1
9350.2.a.e 1
9350.2.a.f 1
9350.2.a.g 1
9350.2.a.h 1
9350.2.a.i 1
9350.2.a.j 1
9350.2.a.k 1
9350.2.a.l 1
9350.2.a.m 1
9350.2.a.n 1
9350.2.a.o 1
9350.2.a.p 1
9350.2.a.q 1
9350.2.a.r 1
9350.2.a.s 1
9350.2.a.t 1
9350.2.a.u 1
9350.2.a.v 1
9350.2.a.w 1
9350.2.a.x 1
9350.2.a.y 1
9350.2.a.z 1
9350.2.a.ba 1
9350.2.a.bb 1
9350.2.a.bc 1
9350.2.a.bd 1
9350.2.a.be 1
9350.2.a.bf 1
9350.2.a.bg 1
9350.2.a.bh 1
9350.2.a.bi 1
9350.2.a.bj 1
9350.2.a.bk 1
9350.2.a.bl 1
9350.2.a.bm 2
9350.2.a.bn 2
9350.2.a.bo 2
9350.2.a.bp 2
9350.2.a.bq 2
9350.2.a.br 2
9350.2.a.bs 2
9350.2.a.bt 2
9350.2.a.bu 2
9350.2.a.bv 2
9350.2.a.bw 3
9350.2.a.bx 3
9350.2.a.by 3
9350.2.a.bz 3
9350.2.a.ca 3
9350.2.a.cb 3
9350.2.a.cc 3
9350.2.a.cd 3
9350.2.a.ce 3
9350.2.a.cf 3
9350.2.a.cg 3
9350.2.a.ch 4
9350.2.a.ci 4
9350.2.a.cj 4
9350.2.a.ck 4
9350.2.a.cl 4
9350.2.a.cm 5
9350.2.a.cn 5
9350.2.a.co 5
9350.2.a.cp 5
9350.2.a.cq 5
9350.2.a.cr 5
9350.2.a.cs 5
9350.2.a.ct 5
9350.2.a.cu 5
9350.2.a.cv 5
9350.2.a.cw 5
9350.2.a.cx 6
9350.2.a.cy 6
9350.2.a.cz 6
9350.2.a.da 6
9350.2.a.db 7
9350.2.a.dc 7
9350.2.a.dd 13
9350.2.a.de 13
9350.2.a.df 13
9350.2.a.dg 13
9350.2.b \(\chi_{9350}(749, \cdot)\) n/a 240 1
9350.2.c \(\chi_{9350}(6051, \cdot)\) n/a 286 1
9350.2.h \(\chi_{9350}(6799, \cdot)\) n/a 268 1
9350.2.j \(\chi_{9350}(5257, \cdot)\) n/a 648 2
9350.2.k \(\chi_{9350}(1849, \cdot)\) n/a 536 2
9350.2.o \(\chi_{9350}(2243, \cdot)\) n/a 648 2
9350.2.p \(\chi_{9350}(307, \cdot)\) n/a 576 2
9350.2.q \(\chi_{9350}(1101, \cdot)\) n/a 572 2
9350.2.s \(\chi_{9350}(1143, \cdot)\) n/a 648 2
9350.2.u \(\chi_{9350}(511, \cdot)\) n/a 1920 4
9350.2.v \(\chi_{9350}(2721, \cdot)\) n/a 1920 4
9350.2.w \(\chi_{9350}(851, \cdot)\) n/a 1216 4
9350.2.x \(\chi_{9350}(1191, \cdot)\) n/a 1920 4
9350.2.y \(\chi_{9350}(1871, \cdot)\) n/a 1600 4
9350.2.z \(\chi_{9350}(1021, \cdot)\) n/a 1920 4
9350.2.ba \(\chi_{9350}(1651, \cdot)\) n/a 1136 4
9350.2.be \(\chi_{9350}(593, \cdot)\) n/a 1296 4
9350.2.bf \(\chi_{9350}(43, \cdot)\) n/a 1296 4
9350.2.bg \(\chi_{9350}(2399, \cdot)\) n/a 1088 4
9350.2.bk \(\chi_{9350}(1939, \cdot)\) n/a 1920 4
9350.2.bl \(\chi_{9350}(1291, \cdot)\) n/a 2160 4
9350.2.bo \(\chi_{9350}(339, \cdot)\) n/a 2160 4
9350.2.bp \(\chi_{9350}(169, \cdot)\) n/a 2160 4
9350.2.bq \(\chi_{9350}(1699, \cdot)\) n/a 1296 4
9350.2.br \(\chi_{9350}(509, \cdot)\) n/a 2160 4
9350.2.ca \(\chi_{9350}(1189, \cdot)\) n/a 1808 4
9350.2.cb \(\chi_{9350}(441, \cdot)\) n/a 1792 4
9350.2.cc \(\chi_{9350}(2619, \cdot)\) n/a 1600 4
9350.2.cl \(\chi_{9350}(1461, \cdot)\) n/a 2160 4
9350.2.cm \(\chi_{9350}(5031, \cdot)\) n/a 2160 4
9350.2.cn \(\chi_{9350}(951, \cdot)\) n/a 1368 4
9350.2.co \(\chi_{9350}(2821, \cdot)\) n/a 2160 4
9350.2.cp \(\chi_{9350}(3469, \cdot)\) n/a 1920 4
9350.2.cq \(\chi_{9350}(69, \cdot)\) n/a 1920 4
9350.2.cr \(\chi_{9350}(1599, \cdot)\) n/a 1152 4
9350.2.cs \(\chi_{9350}(1769, \cdot)\) n/a 1920 4
9350.2.cv \(\chi_{9350}(3569, \cdot)\) n/a 2160 4
9350.2.cz \(\chi_{9350}(243, \cdot)\) n/a 2160 8
9350.2.db \(\chi_{9350}(351, \cdot)\) n/a 2736 8
9350.2.dd \(\chi_{9350}(549, \cdot)\) n/a 2592 8
9350.2.de \(\chi_{9350}(507, \cdot)\) n/a 2160 8
9350.2.dg \(\chi_{9350}(327, \cdot)\) n/a 4320 8
9350.2.di \(\chi_{9350}(3013, \cdot)\) n/a 4320 8
9350.2.dn \(\chi_{9350}(897, \cdot)\) n/a 4320 8
9350.2.do \(\chi_{9350}(293, \cdot)\) n/a 2592 8
9350.2.dp \(\chi_{9350}(387, \cdot)\) n/a 4320 8
9350.2.dq \(\chi_{9350}(123, \cdot)\) n/a 4320 8
9350.2.dt \(\chi_{9350}(2469, \cdot)\) n/a 4320 8
9350.2.du \(\chi_{9350}(1667, \cdot)\) n/a 3840 8
9350.2.dv \(\chi_{9350}(1427, \cdot)\) n/a 4320 8
9350.2.dz \(\chi_{9350}(191, \cdot)\) n/a 4320 8
9350.2.ea \(\chi_{9350}(1721, \cdot)\) n/a 4320 8
9350.2.ef \(\chi_{9350}(1211, \cdot)\) n/a 3584 8
9350.2.eg \(\chi_{9350}(81, \cdot)\) n/a 4320 8
9350.2.eh \(\chi_{9350}(361, \cdot)\) n/a 4320 8
9350.2.ei \(\chi_{9350}(251, \cdot)\) n/a 2736 8
9350.2.em \(\chi_{9350}(1157, \cdot)\) n/a 2304 8
9350.2.en \(\chi_{9350}(1393, \cdot)\) n/a 2592 8
9350.2.eo \(\chi_{9350}(1803, \cdot)\) n/a 3840 8
9350.2.ep \(\chi_{9350}(4353, \cdot)\) n/a 3840 8
9350.2.eq \(\chi_{9350}(953, \cdot)\) n/a 3840 8
9350.2.er \(\chi_{9350}(237, \cdot)\) n/a 4320 8
9350.2.es \(\chi_{9350}(373, \cdot)\) n/a 4320 8
9350.2.et \(\chi_{9350}(1053, \cdot)\) n/a 4320 8
9350.2.fc \(\chi_{9350}(3467, \cdot)\) n/a 4320 8
9350.2.fd \(\chi_{9350}(613, \cdot)\) n/a 3840 8
9350.2.fe \(\chi_{9350}(939, \cdot)\) n/a 4320 8
9350.2.fj \(\chi_{9350}(89, \cdot)\) n/a 3616 8
9350.2.fk \(\chi_{9350}(829, \cdot)\) n/a 4320 8
9350.2.fl \(\chi_{9350}(489, \cdot)\) n/a 4320 8
9350.2.fm \(\chi_{9350}(599, \cdot)\) n/a 2592 8
9350.2.fp \(\chi_{9350}(1713, \cdot)\) n/a 4320 8
9350.2.fq \(\chi_{9350}(1007, \cdot)\) n/a 2592 8
9350.2.fr \(\chi_{9350}(2053, \cdot)\) n/a 4320 8
9350.2.fs \(\chi_{9350}(13, \cdot)\) n/a 4320 8
9350.2.fx \(\chi_{9350}(1033, \cdot)\) n/a 4320 8
9350.2.fz \(\chi_{9350}(633, \cdot)\) n/a 4320 8
9350.2.gb \(\chi_{9350}(2671, \cdot)\) n/a 8640 16
9350.2.gc \(\chi_{9350}(49, \cdot)\) n/a 5184 16
9350.2.gh \(\chi_{9350}(9, \cdot)\) n/a 8640 16
9350.2.gi \(\chi_{9350}(1379, \cdot)\) n/a 8640 16
9350.2.gj \(\chi_{9350}(529, \cdot)\) n/a 7168 16
9350.2.gk \(\chi_{9350}(389, \cdot)\) n/a 8640 16
9350.2.go \(\chi_{9350}(127, \cdot)\) n/a 8640 16
9350.2.gp \(\chi_{9350}(1267, \cdot)\) n/a 8640 16
9350.2.gq \(\chi_{9350}(83, \cdot)\) n/a 8640 16
9350.2.gr \(\chi_{9350}(1317, \cdot)\) n/a 8640 16
9350.2.gs \(\chi_{9350}(417, \cdot)\) n/a 8640 16
9350.2.gt \(\chi_{9350}(1403, \cdot)\) n/a 8640 16
9350.2.gu \(\chi_{9350}(723, \cdot)\) n/a 8640 16
9350.2.gv \(\chi_{9350}(87, \cdot)\) n/a 8640 16
9350.2.gw \(\chi_{9350}(767, \cdot)\) n/a 8640 16
9350.2.gx \(\chi_{9350}(117, \cdot)\) n/a 8640 16
9350.2.hi \(\chi_{9350}(393, \cdot)\) n/a 5184 16
9350.2.hj \(\chi_{9350}(457, \cdot)\) n/a 5184 16
9350.2.hk \(\chi_{9350}(801, \cdot)\) n/a 5472 16
9350.2.hp \(\chi_{9350}(631, \cdot)\) n/a 8640 16
9350.2.hq \(\chi_{9350}(291, \cdot)\) n/a 8640 16
9350.2.hr \(\chi_{9350}(111, \cdot)\) n/a 7232 16
9350.2.hs \(\chi_{9350}(621, \cdot)\) n/a 8640 16
9350.2.hv \(\chi_{9350}(59, \cdot)\) n/a 8640 16
9350.2.hx \(\chi_{9350}(1083, \cdot)\) n/a 17280 32
9350.2.id \(\chi_{9350}(113, \cdot)\) n/a 17280 32
9350.2.ie \(\chi_{9350}(23, \cdot)\) n/a 14400 32
9350.2.if \(\chi_{9350}(163, \cdot)\) n/a 17280 32
9350.2.ig \(\chi_{9350}(207, \cdot)\) n/a 10368 32
9350.2.ih \(\chi_{9350}(267, \cdot)\) n/a 17280 32
9350.2.ii \(\chi_{9350}(601, \cdot)\) n/a 10944 32
9350.2.il \(\chi_{9350}(79, \cdot)\) n/a 17280 32
9350.2.im \(\chi_{9350}(29, \cdot)\) n/a 17280 32
9350.2.in \(\chi_{9350}(39, \cdot)\) n/a 17280 32
9350.2.ir \(\chi_{9350}(109, \cdot)\) n/a 17280 32
9350.2.is \(\chi_{9350}(139, \cdot)\) n/a 17280 32
9350.2.iv \(\chi_{9350}(261, \cdot)\) n/a 17280 32
9350.2.iw \(\chi_{9350}(211, \cdot)\) n/a 17280 32
9350.2.ix \(\chi_{9350}(61, \cdot)\) n/a 17280 32
9350.2.jb \(\chi_{9350}(131, \cdot)\) n/a 17280 32
9350.2.jc \(\chi_{9350}(41, \cdot)\) n/a 17280 32
9350.2.je \(\chi_{9350}(249, \cdot)\) n/a 10368 32
9350.2.jg \(\chi_{9350}(317, \cdot)\) n/a 17280 32
9350.2.jh \(\chi_{9350}(133, \cdot)\) n/a 14400 32
9350.2.ji \(\chi_{9350}(3, \cdot)\) n/a 17280 32
9350.2.jj \(\chi_{9350}(643, \cdot)\) n/a 10368 32
9350.2.jk \(\chi_{9350}(147, \cdot)\) n/a 17280 32
9350.2.jq \(\chi_{9350}(37, \cdot)\) n/a 17280 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9350))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9350)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(187))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(374))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(850))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(935))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1870))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4675))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9350))\)\(^{\oplus 1}\)