↑

Properties

Label 9150.2
Level 9150
Weight 2
Dimension 514016
Nonzero newspaces 140
Sturm bound 8928000

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 9150 = 2 \cdot 3 \cdot 5^{2} \cdot 61 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 140 \)
Sturm bound: \(8928000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9150))\).

Total New Old
Modular forms 2245440 514016 1731424
Cusp forms 2218561 514016 1704545
Eisenstein series 26879 0 26879

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9150))\)

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
9150.2.a \(\chi_{9150}(1, \cdot)\) 9150.2.a.a 1 1
9150.2.a.b 1
9150.2.a.c 1
9150.2.a.d 1
9150.2.a.e 1
9150.2.a.f 1
9150.2.a.g 1
9150.2.a.h 1
9150.2.a.i 1
9150.2.a.j 1
9150.2.a.k 1
9150.2.a.l 1
9150.2.a.m 1
9150.2.a.n 1
9150.2.a.o 1
9150.2.a.p 1
9150.2.a.q 1
9150.2.a.r 1
9150.2.a.s 1
9150.2.a.t 1
9150.2.a.u 1
9150.2.a.v 1
9150.2.a.w 1
9150.2.a.x 1
9150.2.a.y 1
9150.2.a.z 1
9150.2.a.ba 1
9150.2.a.bb 2
9150.2.a.bc 2
9150.2.a.bd 2
9150.2.a.be 2
9150.2.a.bf 2
9150.2.a.bg 2
9150.2.a.bh 2
9150.2.a.bi 3
9150.2.a.bj 3
9150.2.a.bk 3
9150.2.a.bl 3
9150.2.a.bm 3
9150.2.a.bn 4
9150.2.a.bo 4
9150.2.a.bp 5
9150.2.a.bq 5
9150.2.a.br 5
9150.2.a.bs 5
9150.2.a.bt 5
9150.2.a.bu 5
9150.2.a.bv 5
9150.2.a.bw 5
9150.2.a.bx 5
9150.2.a.by 5
9150.2.a.bz 5
9150.2.a.ca 5
9150.2.a.cb 5
9150.2.a.cc 5
9150.2.a.cd 5
9150.2.a.ce 5
9150.2.a.cf 6
9150.2.a.cg 6
9150.2.a.ch 8
9150.2.a.ci 8
9150.2.a.cj 9
9150.2.a.ck 9
9150.2.c \(\chi_{9150}(1951, \cdot)\) n/a 194 1
9150.2.d \(\chi_{9150}(1099, \cdot)\) n/a 180 1
9150.2.f \(\chi_{9150}(3049, \cdot)\) n/a 188 1
9150.2.i \(\chi_{9150}(901, \cdot)\) n/a 396 2
9150.2.k \(\chi_{9150}(5257, \cdot)\) n/a 372 2
9150.2.m \(\chi_{9150}(1343, \cdot)\) n/a 720 2
9150.2.o \(\chi_{9150}(599, \cdot)\) n/a 744 2
9150.2.q \(\chi_{9150}(5501, \cdot)\) n/a 788 2
9150.2.r \(\chi_{9150}(3293, \cdot)\) n/a 744 2
9150.2.t \(\chi_{9150}(3793, \cdot)\) n/a 372 2
9150.2.v \(\chi_{9150}(2521, \cdot)\) n/a 1232 4
9150.2.w \(\chi_{9150}(241, \cdot)\) n/a 1232 4
9150.2.x \(\chi_{9150}(691, \cdot)\) n/a 1232 4
9150.2.y \(\chi_{9150}(2071, \cdot)\) n/a 1232 4
9150.2.z \(\chi_{9150}(1351, \cdot)\) n/a 784 4
9150.2.ba \(\chi_{9150}(1831, \cdot)\) n/a 1200 4
9150.2.bc \(\chi_{9150}(2149, \cdot)\) n/a 376 2
9150.2.be \(\chi_{9150}(1051, \cdot)\) n/a 392 2
9150.2.bh \(\chi_{9150}(1999, \cdot)\) n/a 368 2
9150.2.bj \(\chi_{9150}(2929, \cdot)\) n/a 1200 4
9150.2.bk \(\chi_{9150}(121, \cdot)\) n/a 1248 4
9150.2.bm \(\chi_{9150}(1699, \cdot)\) n/a 752 4
9150.2.bw \(\chi_{9150}(2809, \cdot)\) n/a 1232 4
9150.2.bx \(\chi_{9150}(529, \cdot)\) n/a 1232 4
9150.2.by \(\chi_{9150}(1369, \cdot)\) n/a 1232 4
9150.2.bz \(\chi_{9150}(979, \cdot)\) n/a 1232 4
9150.2.cc \(\chi_{9150}(601, \cdot)\) n/a 776 4
9150.2.ch \(\chi_{9150}(3619, \cdot)\) n/a 1248 4
9150.2.ci \(\chi_{9150}(3169, \cdot)\) n/a 1248 4
9150.2.cj \(\chi_{9150}(619, \cdot)\) n/a 1248 4
9150.2.ck \(\chi_{9150}(1339, \cdot)\) n/a 1248 4
9150.2.cl \(\chi_{9150}(5371, \cdot)\) n/a 1248 4
9150.2.cm \(\chi_{9150}(271, \cdot)\) n/a 1248 4
9150.2.cn \(\chi_{9150}(4261, \cdot)\) n/a 1248 4
9150.2.co \(\chi_{9150}(1711, \cdot)\) n/a 1248 4
9150.2.ct \(\chi_{9150}(949, \cdot)\) n/a 736 4
9150.2.cx \(\chi_{9150}(1219, \cdot)\) n/a 1232 4
9150.2.cz \(\chi_{9150}(3193, \cdot)\) n/a 744 4
9150.2.da \(\chi_{9150}(257, \cdot)\) n/a 1488 4
9150.2.dd \(\chi_{9150}(101, \cdot)\) n/a 1568 4
9150.2.df \(\chi_{9150}(1199, \cdot)\) n/a 1488 4
9150.2.dh \(\chi_{9150}(2393, \cdot)\) n/a 1488 4
9150.2.di \(\chi_{9150}(4657, \cdot)\) n/a 744 4
9150.2.dk \(\chi_{9150}(1111, \cdot)\) n/a 2464 8
9150.2.dl \(\chi_{9150}(571, \cdot)\) n/a 2464 8
9150.2.dm \(\chi_{9150}(391, \cdot)\) n/a 2464 8
9150.2.dn \(\chi_{9150}(1171, \cdot)\) n/a 2464 8
9150.2.do \(\chi_{9150}(361, \cdot)\) n/a 2464 8
9150.2.dp \(\chi_{9150}(301, \cdot)\) n/a 1584 8
9150.2.dq \(\chi_{9150}(1453, \cdot)\) n/a 2480 8
9150.2.ds \(\chi_{9150}(817, \cdot)\) n/a 2480 8
9150.2.dx \(\chi_{9150}(313, \cdot)\) n/a 2480 8
9150.2.dy \(\chi_{9150}(3937, \cdot)\) n/a 2480 8
9150.2.dz \(\chi_{9150}(343, \cdot)\) n/a 1488 8
9150.2.ea \(\chi_{9150}(277, \cdot)\) n/a 2480 8
9150.2.ec \(\chi_{9150}(1193, \cdot)\) n/a 2976 8
9150.2.ef \(\chi_{9150}(1223, \cdot)\) n/a 4960 8
9150.2.eg \(\chi_{9150}(773, \cdot)\) n/a 4960 8
9150.2.ek \(\chi_{9150}(1577, \cdot)\) n/a 4960 8
9150.2.el \(\chi_{9150}(1097, \cdot)\) n/a 4960 8
9150.2.em \(\chi_{9150}(113, \cdot)\) n/a 4960 8
9150.2.eo \(\chi_{9150}(2249, \cdot)\) n/a 2976 8
9150.2.eq \(\chi_{9150}(221, \cdot)\) n/a 4960 8
9150.2.et \(\chi_{9150}(11, \cdot)\) n/a 4960 8
9150.2.eu \(\chi_{9150}(281, \cdot)\) n/a 4960 8
9150.2.ev \(\chi_{9150}(1061, \cdot)\) n/a 4960 8
9150.2.ez \(\chi_{9150}(191, \cdot)\) n/a 4960 8
9150.2.fa \(\chi_{9150}(89, \cdot)\) n/a 4960 8
9150.2.fd \(\chi_{9150}(1109, \cdot)\) n/a 4960 8
9150.2.fe \(\chi_{9150}(1319, \cdot)\) n/a 4960 8
9150.2.ff \(\chi_{9150}(1289, \cdot)\) n/a 4960 8
9150.2.fj \(\chi_{9150}(329, \cdot)\) n/a 4960 8
9150.2.fk \(\chi_{9150}(1151, \cdot)\) n/a 3152 8
9150.2.fm \(\chi_{9150}(497, \cdot)\) n/a 4960 8
9150.2.fp \(\chi_{9150}(203, \cdot)\) n/a 4960 8
9150.2.fq \(\chi_{9150}(977, \cdot)\) n/a 4800 8
9150.2.fr \(\chi_{9150}(827, \cdot)\) n/a 4960 8
9150.2.fv \(\chi_{9150}(3413, \cdot)\) n/a 4960 8
9150.2.fx \(\chi_{9150}(407, \cdot)\) n/a 2976 8
9150.2.fz \(\chi_{9150}(3103, \cdot)\) n/a 2480 8
9150.2.ga \(\chi_{9150}(643, \cdot)\) n/a 1488 8
9150.2.gb \(\chi_{9150}(3073, \cdot)\) n/a 2480 8
9150.2.gc \(\chi_{9150}(37, \cdot)\) n/a 2480 8
9150.2.gh \(\chi_{9150}(1183, \cdot)\) n/a 2480 8
9150.2.gj \(\chi_{9150}(133, \cdot)\) n/a 2480 8
9150.2.gl \(\chi_{9150}(109, \cdot)\) n/a 2464 8
9150.2.gn \(\chi_{9150}(751, \cdot)\) n/a 1568 8
9150.2.gp \(\chi_{9150}(2269, \cdot)\) n/a 2496 8
9150.2.gq \(\chi_{9150}(1489, \cdot)\) n/a 2496 8
9150.2.gr \(\chi_{9150}(259, \cdot)\) n/a 2496 8
9150.2.gs \(\chi_{9150}(439, \cdot)\) n/a 2496 8
9150.2.hb \(\chi_{9150}(781, \cdot)\) n/a 2496 8
9150.2.hc \(\chi_{9150}(1021, \cdot)\) n/a 2496 8
9150.2.hd \(\chi_{9150}(1561, \cdot)\) n/a 2496 8
9150.2.he \(\chi_{9150}(961, \cdot)\) n/a 2496 8
9150.2.hg \(\chi_{9150}(199, \cdot)\) n/a 1472 8
9150.2.hi \(\chi_{9150}(49, \cdot)\) n/a 1504 8
9150.2.hn \(\chi_{9150}(859, \cdot)\) n/a 2464 8
9150.2.ho \(\chi_{9150}(2659, \cdot)\) n/a 2464 8
9150.2.hp \(\chi_{9150}(19, \cdot)\) n/a 2464 8
9150.2.hq \(\chi_{9150}(229, \cdot)\) n/a 2464 8
9150.2.hw \(\chi_{9150}(169, \cdot)\) n/a 2496 8
9150.2.hz \(\chi_{9150}(841, \cdot)\) n/a 2496 8
9150.2.ia \(\chi_{9150}(337, \cdot)\) n/a 4960 16
9150.2.ic \(\chi_{9150}(547, \cdot)\) n/a 4960 16
9150.2.ih \(\chi_{9150}(673, \cdot)\) n/a 4960 16
9150.2.ii \(\chi_{9150}(157, \cdot)\) n/a 2976 16
9150.2.ij \(\chi_{9150}(67, \cdot)\) n/a 4960 16
9150.2.ik \(\chi_{9150}(397, \cdot)\) n/a 4960 16
9150.2.in \(\chi_{9150}(443, \cdot)\) n/a 5952 16
9150.2.ip \(\chi_{9150}(1937, \cdot)\) n/a 9920 16
9150.2.iq \(\chi_{9150}(167, \cdot)\) n/a 9920 16
9150.2.ir \(\chi_{9150}(197, \cdot)\) n/a 9920 16
9150.2.iv \(\chi_{9150}(263, \cdot)\) n/a 9920 16
9150.2.iw \(\chi_{9150}(527, \cdot)\) n/a 9920 16
9150.2.iy \(\chi_{9150}(251, \cdot)\) n/a 6272 16
9150.2.jb \(\chi_{9150}(539, \cdot)\) n/a 9920 16
9150.2.jc \(\chi_{9150}(59, \cdot)\) n/a 9920 16
9150.2.jd \(\chi_{9150}(29, \cdot)\) n/a 9920 16
9150.2.jh \(\chi_{9150}(2789, \cdot)\) n/a 9920 16
9150.2.ji \(\chi_{9150}(359, \cdot)\) n/a 9920 16
9150.2.jl \(\chi_{9150}(71, \cdot)\) n/a 9920 16
9150.2.jm \(\chi_{9150}(1691, \cdot)\) n/a 9920 16
9150.2.jn \(\chi_{9150}(581, \cdot)\) n/a 9920 16
9150.2.jr \(\chi_{9150}(311, \cdot)\) n/a 9920 16
9150.2.js \(\chi_{9150}(641, \cdot)\) n/a 9920 16
9150.2.ju \(\chi_{9150}(299, \cdot)\) n/a 5952 16
9150.2.jw \(\chi_{9150}(77, \cdot)\) n/a 9920 16
9150.2.ka \(\chi_{9150}(83, \cdot)\) n/a 9920 16
9150.2.kb \(\chi_{9150}(347, \cdot)\) n/a 9920 16
9150.2.kc \(\chi_{9150}(47, \cdot)\) n/a 9920 16
9150.2.kf \(\chi_{9150}(317, \cdot)\) n/a 9920 16
9150.2.kg \(\chi_{9150}(107, \cdot)\) n/a 5952 16
9150.2.kj \(\chi_{9150}(523, \cdot)\) n/a 4960 16
9150.2.kk \(\chi_{9150}(3277, \cdot)\) n/a 4960 16
9150.2.kl \(\chi_{9150}(7, \cdot)\) n/a 2976 16
9150.2.km \(\chi_{9150}(433, \cdot)\) n/a 4960 16
9150.2.kr \(\chi_{9150}(697, \cdot)\) n/a 4960 16
9150.2.kt \(\chi_{9150}(223, \cdot)\) n/a 4960 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9150))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9150)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(61))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(122))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(183))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(305))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(366))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(610))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(915))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1525))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1830))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3050))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4575))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9150))\)\(^{\oplus 1}\)