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Properties

Label 9300.2
Level 9300
Weight 2
Dimension 924728
Nonzero newspaces 168
Sturm bound 9216000

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Defining parameters

Level: \( N \) = \( 9300 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 168 \)
Sturm bound: \(9216000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9300))\).

Total New Old
Modular forms 2320800 929480 1391320
Cusp forms 2287201 924728 1362473
Eisenstein series 33599 4752 28847

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9300))\)

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
9300.2.a \(\chi_{9300}(1, \cdot)\) 9300.2.a.a 1 1
9300.2.a.b 1
9300.2.a.c 1
9300.2.a.d 1
9300.2.a.e 1
9300.2.a.f 1
9300.2.a.g 1
9300.2.a.h 1
9300.2.a.i 1
9300.2.a.j 1
9300.2.a.k 1
9300.2.a.l 1
9300.2.a.m 1
9300.2.a.n 2
9300.2.a.o 2
9300.2.a.p 2
9300.2.a.q 2
9300.2.a.r 2
9300.2.a.s 3
9300.2.a.t 3
9300.2.a.u 3
9300.2.a.v 3
9300.2.a.w 3
9300.2.a.x 4
9300.2.a.y 6
9300.2.a.z 6
9300.2.a.ba 6
9300.2.a.bb 6
9300.2.a.bc 7
9300.2.a.bd 7
9300.2.a.be 7
9300.2.a.bf 7
9300.2.f \(\chi_{9300}(2851, \cdot)\) n/a 608 1
9300.2.g \(\chi_{9300}(3349, \cdot)\) 9300.2.g.a 2 1
9300.2.g.b 2
9300.2.g.c 2
9300.2.g.d 2
9300.2.g.e 2
9300.2.g.f 2
9300.2.g.g 2
9300.2.g.h 2
9300.2.g.i 2
9300.2.g.j 2
9300.2.g.k 4
9300.2.g.l 4
9300.2.g.m 4
9300.2.g.n 4
9300.2.g.o 6
9300.2.g.p 6
9300.2.g.q 6
9300.2.g.r 6
9300.2.g.s 8
9300.2.g.t 12
9300.2.g.u 12
9300.2.h \(\chi_{9300}(7751, \cdot)\) n/a 1140 1
9300.2.i \(\chi_{9300}(4649, \cdot)\) n/a 192 1
9300.2.n \(\chi_{9300}(1799, \cdot)\) n/a 1080 1
9300.2.o \(\chi_{9300}(1301, \cdot)\) n/a 202 1
9300.2.p \(\chi_{9300}(6199, \cdot)\) n/a 576 1
9300.2.q \(\chi_{9300}(3001, \cdot)\) n/a 202 2
9300.2.r \(\chi_{9300}(2357, \cdot)\) n/a 360 2
9300.2.s \(\chi_{9300}(2293, \cdot)\) n/a 192 2
9300.2.t \(\chi_{9300}(743, \cdot)\) n/a 2288 2
9300.2.u \(\chi_{9300}(3907, \cdot)\) n/a 1080 2
9300.2.z \(\chi_{9300}(721, \cdot)\) n/a 640 4
9300.2.ba \(\chi_{9300}(901, \cdot)\) n/a 408 4
9300.2.bb \(\chi_{9300}(4441, \cdot)\) n/a 640 4
9300.2.bc \(\chi_{9300}(2341, \cdot)\) n/a 640 4
9300.2.bd \(\chi_{9300}(481, \cdot)\) n/a 640 4
9300.2.be \(\chi_{9300}(1861, \cdot)\) n/a 608 4
9300.2.bf \(\chi_{9300}(2599, \cdot)\) n/a 1152 2
9300.2.bg \(\chi_{9300}(7001, \cdot)\) n/a 406 2
9300.2.bh \(\chi_{9300}(4799, \cdot)\) n/a 2288 2
9300.2.bm \(\chi_{9300}(1049, \cdot)\) n/a 384 2
9300.2.bn \(\chi_{9300}(1451, \cdot)\) n/a 2408 2
9300.2.bo \(\chi_{9300}(6349, \cdot)\) n/a 192 2
9300.2.bp \(\chi_{9300}(8551, \cdot)\) n/a 1216 2
9300.2.bu \(\chi_{9300}(929, \cdot)\) n/a 1280 4
9300.2.bv \(\chi_{9300}(311, \cdot)\) n/a 7200 4
9300.2.bw \(\chi_{9300}(1489, \cdot)\) n/a 592 4
9300.2.bx \(\chi_{9300}(991, \cdot)\) n/a 3840 4
9300.2.cg \(\chi_{9300}(581, \cdot)\) n/a 1280 4
9300.2.ch \(\chi_{9300}(779, \cdot)\) n/a 7648 4
9300.2.ci \(\chi_{9300}(1639, \cdot)\) n/a 3840 4
9300.2.cj \(\chi_{9300}(139, \cdot)\) n/a 3840 4
9300.2.ck \(\chi_{9300}(1999, \cdot)\) n/a 2304 4
9300.2.cl \(\chi_{9300}(401, \cdot)\) n/a 808 4
9300.2.cm \(\chi_{9300}(4181, \cdot)\) n/a 1280 4
9300.2.cn \(\chi_{9300}(461, \cdot)\) n/a 1280 4
9300.2.co \(\chi_{9300}(659, \cdot)\) n/a 7648 4
9300.2.cp \(\chi_{9300}(2699, \cdot)\) n/a 4576 4
9300.2.cq \(\chi_{9300}(4139, \cdot)\) n/a 7648 4
9300.2.cr \(\chi_{9300}(3439, \cdot)\) n/a 3840 4
9300.2.di \(\chi_{9300}(1579, \cdot)\) n/a 3840 4
9300.2.dj \(\chi_{9300}(419, \cdot)\) n/a 7648 4
9300.2.dk \(\chi_{9300}(2681, \cdot)\) n/a 1280 4
9300.2.dp \(\chi_{9300}(109, \cdot)\) n/a 640 4
9300.2.dq \(\chi_{9300}(2131, \cdot)\) n/a 3840 4
9300.2.dr \(\chi_{9300}(89, \cdot)\) n/a 1280 4
9300.2.ds \(\chi_{9300}(3929, \cdot)\) n/a 1280 4
9300.2.dt \(\chi_{9300}(449, \cdot)\) n/a 768 4
9300.2.du \(\chi_{9300}(4511, \cdot)\) n/a 7648 4
9300.2.dv \(\chi_{9300}(1151, \cdot)\) n/a 4816 4
9300.2.dw \(\chi_{9300}(2891, \cdot)\) n/a 7648 4
9300.2.dx \(\chi_{9300}(2209, \cdot)\) n/a 640 4
9300.2.dy \(\chi_{9300}(349, \cdot)\) n/a 384 4
9300.2.dz \(\chi_{9300}(469, \cdot)\) n/a 640 4
9300.2.ea \(\chi_{9300}(151, \cdot)\) n/a 2432 4
9300.2.eb \(\chi_{9300}(91, \cdot)\) n/a 3840 4
9300.2.ec \(\chi_{9300}(2011, \cdot)\) n/a 3840 4
9300.2.ed \(\chi_{9300}(1889, \cdot)\) n/a 1280 4
9300.2.ee \(\chi_{9300}(791, \cdot)\) n/a 7648 4
9300.2.ev \(\chi_{9300}(3071, \cdot)\) n/a 7648 4
9300.2.ew \(\chi_{9300}(29, \cdot)\) n/a 1280 4
9300.2.ex \(\chi_{9300}(4231, \cdot)\) n/a 3840 4
9300.2.ey \(\chi_{9300}(529, \cdot)\) n/a 640 4
9300.2.ez \(\chi_{9300}(619, \cdot)\) n/a 3840 4
9300.2.fa \(\chi_{9300}(3161, \cdot)\) n/a 1280 4
9300.2.fb \(\chi_{9300}(3659, \cdot)\) n/a 7200 4
9300.2.fk \(\chi_{9300}(2443, \cdot)\) n/a 2304 4
9300.2.fl \(\chi_{9300}(1607, \cdot)\) n/a 4576 4
9300.2.fm \(\chi_{9300}(3157, \cdot)\) n/a 384 4
9300.2.fn \(\chi_{9300}(893, \cdot)\) n/a 768 4
9300.2.fo \(\chi_{9300}(1141, \cdot)\) n/a 1280 8
9300.2.fp \(\chi_{9300}(1321, \cdot)\) n/a 1280 8
9300.2.fq \(\chi_{9300}(661, \cdot)\) n/a 1280 8
9300.2.fr \(\chi_{9300}(2401, \cdot)\) n/a 808 8
9300.2.fs \(\chi_{9300}(1621, \cdot)\) n/a 1280 8
9300.2.ft \(\chi_{9300}(121, \cdot)\) n/a 1280 8
9300.2.fu \(\chi_{9300}(337, \cdot)\) n/a 1280 8
9300.2.fv \(\chi_{9300}(233, \cdot)\) n/a 2560 8
9300.2.fw \(\chi_{9300}(667, \cdot)\) n/a 7680 8
9300.2.fx \(\chi_{9300}(23, \cdot)\) n/a 15296 8
9300.2.gs \(\chi_{9300}(163, \cdot)\) n/a 7680 8
9300.2.gt \(\chi_{9300}(3623, \cdot)\) n/a 15296 8
9300.2.gu \(\chi_{9300}(587, \cdot)\) n/a 15296 8
9300.2.gv \(\chi_{9300}(187, \cdot)\) n/a 7200 8
9300.2.gw \(\chi_{9300}(343, \cdot)\) n/a 4608 8
9300.2.gx \(\chi_{9300}(2767, \cdot)\) n/a 7680 8
9300.2.gy \(\chi_{9300}(1487, \cdot)\) n/a 15296 8
9300.2.gz \(\chi_{9300}(263, \cdot)\) n/a 15296 8
9300.2.ha \(\chi_{9300}(1007, \cdot)\) n/a 9152 8
9300.2.hb \(\chi_{9300}(283, \cdot)\) n/a 7680 8
9300.2.hc \(\chi_{9300}(977, \cdot)\) n/a 2560 8
9300.2.hd \(\chi_{9300}(433, \cdot)\) n/a 1280 8
9300.2.he \(\chi_{9300}(277, \cdot)\) n/a 1280 8
9300.2.hf \(\chi_{9300}(457, \cdot)\) n/a 768 8
9300.2.hg \(\chi_{9300}(497, \cdot)\) n/a 2400 8
9300.2.hh \(\chi_{9300}(593, \cdot)\) n/a 1536 8
9300.2.hi \(\chi_{9300}(1217, \cdot)\) n/a 2560 8
9300.2.hj \(\chi_{9300}(2137, \cdot)\) n/a 1280 8
9300.2.hk \(\chi_{9300}(697, \cdot)\) n/a 1280 8
9300.2.hl \(\chi_{9300}(3953, \cdot)\) n/a 2560 8
9300.2.hu \(\chi_{9300}(1079, \cdot)\) n/a 15296 8
9300.2.hv \(\chi_{9300}(161, \cdot)\) n/a 2560 8
9300.2.hw \(\chi_{9300}(739, \cdot)\) n/a 7680 8
9300.2.hx \(\chi_{9300}(1309, \cdot)\) n/a 1280 8
9300.2.hy \(\chi_{9300}(2311, \cdot)\) n/a 7680 8
9300.2.hz \(\chi_{9300}(389, \cdot)\) n/a 2560 8
9300.2.ia \(\chi_{9300}(431, \cdot)\) n/a 15296 8
9300.2.ir \(\chi_{9300}(671, \cdot)\) n/a 15296 8
9300.2.is \(\chi_{9300}(509, \cdot)\) n/a 2560 8
9300.2.it \(\chi_{9300}(631, \cdot)\) n/a 7680 8
9300.2.iu \(\chi_{9300}(451, \cdot)\) n/a 4864 8
9300.2.iv \(\chi_{9300}(331, \cdot)\) n/a 7680 8
9300.2.iw \(\chi_{9300}(3109, \cdot)\) n/a 1280 8
9300.2.ix \(\chi_{9300}(2029, \cdot)\) n/a 1280 8
9300.2.iy \(\chi_{9300}(49, \cdot)\) n/a 768 8
9300.2.iz \(\chi_{9300}(851, \cdot)\) n/a 9632 8
9300.2.ja \(\chi_{9300}(71, \cdot)\) n/a 15296 8
9300.2.jb \(\chi_{9300}(1631, \cdot)\) n/a 15296 8
9300.2.jc \(\chi_{9300}(269, \cdot)\) n/a 2560 8
9300.2.jd \(\chi_{9300}(2249, \cdot)\) n/a 1536 8
9300.2.je \(\chi_{9300}(569, \cdot)\) n/a 2560 8
9300.2.jf \(\chi_{9300}(1171, \cdot)\) n/a 7680 8
9300.2.jg \(\chi_{9300}(169, \cdot)\) n/a 1280 8
9300.2.jl \(\chi_{9300}(761, \cdot)\) n/a 2560 8
9300.2.jm \(\chi_{9300}(1919, \cdot)\) n/a 15296 8
9300.2.jn \(\chi_{9300}(259, \cdot)\) n/a 7680 8
9300.2.ke \(\chi_{9300}(2059, \cdot)\) n/a 7680 8
9300.2.kf \(\chi_{9300}(1559, \cdot)\) n/a 15296 8
9300.2.kg \(\chi_{9300}(479, \cdot)\) n/a 15296 8
9300.2.kh \(\chi_{9300}(299, \cdot)\) n/a 9152 8
9300.2.ki \(\chi_{9300}(641, \cdot)\) n/a 2560 8
9300.2.kj \(\chi_{9300}(2501, \cdot)\) n/a 1624 8
9300.2.kk \(\chi_{9300}(1541, \cdot)\) n/a 2560 8
9300.2.kl \(\chi_{9300}(859, \cdot)\) n/a 7680 8
9300.2.km \(\chi_{9300}(199, \cdot)\) n/a 4608 8
9300.2.kn \(\chi_{9300}(79, \cdot)\) n/a 7680 8
9300.2.ko \(\chi_{9300}(59, \cdot)\) n/a 15296 8
9300.2.kp \(\chi_{9300}(2741, \cdot)\) n/a 2560 8
9300.2.ky \(\chi_{9300}(1111, \cdot)\) n/a 7680 8
9300.2.kz \(\chi_{9300}(769, \cdot)\) n/a 1280 8
9300.2.la \(\chi_{9300}(191, \cdot)\) n/a 15296 8
9300.2.lb \(\chi_{9300}(2909, \cdot)\) n/a 2560 8
9300.2.lg \(\chi_{9300}(817, \cdot)\) n/a 2560 16
9300.2.lh \(\chi_{9300}(1073, \cdot)\) n/a 5120 16
9300.2.li \(\chi_{9300}(257, \cdot)\) n/a 3072 16
9300.2.lj \(\chi_{9300}(377, \cdot)\) n/a 5120 16
9300.2.lk \(\chi_{9300}(757, \cdot)\) n/a 1536 16
9300.2.ll \(\chi_{9300}(13, \cdot)\) n/a 2560 16
9300.2.lm \(\chi_{9300}(37, \cdot)\) n/a 2560 16
9300.2.ln \(\chi_{9300}(173, \cdot)\) n/a 5120 16
9300.2.lo \(\chi_{9300}(1037, \cdot)\) n/a 5120 16
9300.2.lp \(\chi_{9300}(73, \cdot)\) n/a 2560 16
9300.2.lq \(\chi_{9300}(83, \cdot)\) n/a 30592 16
9300.2.lr \(\chi_{9300}(1063, \cdot)\) n/a 15360 16
9300.2.ls \(\chi_{9300}(763, \cdot)\) n/a 15360 16
9300.2.lt \(\chi_{9300}(1943, \cdot)\) n/a 18304 16
9300.2.lu \(\chi_{9300}(827, \cdot)\) n/a 30592 16
9300.2.lv \(\chi_{9300}(347, \cdot)\) n/a 30592 16
9300.2.lw \(\chi_{9300}(547, \cdot)\) n/a 15360 16
9300.2.lx \(\chi_{9300}(7, \cdot)\) n/a 9216 16
9300.2.ly \(\chi_{9300}(67, \cdot)\) n/a 15360 16
9300.2.lz \(\chi_{9300}(203, \cdot)\) n/a 30592 16
9300.2.mu \(\chi_{9300}(1067, \cdot)\) n/a 30592 16
9300.2.mv \(\chi_{9300}(103, \cdot)\) n/a 15360 16
9300.2.mw \(\chi_{9300}(113, \cdot)\) n/a 5120 16
9300.2.mx \(\chi_{9300}(613, \cdot)\) n/a 2560 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9300))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9300)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(372))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(465))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(620))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(775))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(930))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1550))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1860))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2325))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4650))\)\(^{\oplus 2}\)