Properties

Label 9792.2
Level 9792
Weight 2
Dimension 1170774
Nonzero newspaces 136
Sturm bound 10616832

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Defining parameters

Level: \( N \) = \( 9792 = 2^{6} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 136 \)
Sturm bound: \(10616832\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9792))\).

Total New Old
Modular forms 2672640 1176714 1495926
Cusp forms 2635777 1170774 1465003
Eisenstein series 36863 5940 30923

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9792))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
9792.2.a \(\chi_{9792}(1, \cdot)\) 9792.2.a.a 1 1
9792.2.a.b 1
9792.2.a.c 1
9792.2.a.d 1
9792.2.a.e 1
9792.2.a.f 1
9792.2.a.g 1
9792.2.a.h 1
9792.2.a.i 1
9792.2.a.j 1
9792.2.a.k 1
9792.2.a.l 1
9792.2.a.m 1
9792.2.a.n 1
9792.2.a.o 1
9792.2.a.p 1
9792.2.a.q 1
9792.2.a.r 1
9792.2.a.s 1
9792.2.a.t 1
9792.2.a.u 1
9792.2.a.v 1
9792.2.a.w 1
9792.2.a.x 1
9792.2.a.y 1
9792.2.a.z 1
9792.2.a.ba 1
9792.2.a.bb 1
9792.2.a.bc 1
9792.2.a.bd 1
9792.2.a.be 1
9792.2.a.bf 1
9792.2.a.bg 1
9792.2.a.bh 1
9792.2.a.bi 1
9792.2.a.bj 1
9792.2.a.bk 1
9792.2.a.bl 1
9792.2.a.bm 1
9792.2.a.bn 1
9792.2.a.bo 1
9792.2.a.bp 1
9792.2.a.bq 1
9792.2.a.br 1
9792.2.a.bs 1
9792.2.a.bt 1
9792.2.a.bu 1
9792.2.a.bv 1
9792.2.a.bw 1
9792.2.a.bx 1
9792.2.a.by 1
9792.2.a.bz 1
9792.2.a.ca 1
9792.2.a.cb 1
9792.2.a.cc 1
9792.2.a.cd 1
9792.2.a.ce 1
9792.2.a.cf 1
9792.2.a.cg 2
9792.2.a.ch 2
9792.2.a.ci 2
9792.2.a.cj 2
9792.2.a.ck 2
9792.2.a.cl 2
9792.2.a.cm 2
9792.2.a.cn 2
9792.2.a.co 2
9792.2.a.cp 2
9792.2.a.cq 2
9792.2.a.cr 2
9792.2.a.cs 2
9792.2.a.ct 2
9792.2.a.cu 2
9792.2.a.cv 2
9792.2.a.cw 2
9792.2.a.cx 2
9792.2.a.cy 2
9792.2.a.cz 2
9792.2.a.da 2
9792.2.a.db 2
9792.2.a.dc 3
9792.2.a.dd 3
9792.2.a.de 3
9792.2.a.df 3
9792.2.a.dg 3
9792.2.a.dh 3
9792.2.a.di 3
9792.2.a.dj 3
9792.2.a.dk 3
9792.2.a.dl 3
9792.2.a.dm 4
9792.2.a.dn 4
9792.2.a.do 4
9792.2.a.dp 4
9792.2.a.dq 6
9792.2.a.dr 6
9792.2.c \(\chi_{9792}(577, \cdot)\) n/a 178 1
9792.2.e \(\chi_{9792}(9215, \cdot)\) n/a 128 1
9792.2.f \(\chi_{9792}(4897, \cdot)\) n/a 160 1
9792.2.h \(\chi_{9792}(4895, \cdot)\) n/a 144 1
9792.2.j \(\chi_{9792}(4319, \cdot)\) n/a 128 1
9792.2.l \(\chi_{9792}(5473, \cdot)\) n/a 180 1
9792.2.o \(\chi_{9792}(9791, \cdot)\) n/a 144 1
9792.2.q \(\chi_{9792}(3265, \cdot)\) n/a 768 2
9792.2.s \(\chi_{9792}(3311, \cdot)\) n/a 288 2
9792.2.t \(\chi_{9792}(3889, \cdot)\) n/a 356 2
9792.2.v \(\chi_{9792}(2449, \cdot)\) n/a 320 2
9792.2.x \(\chi_{9792}(2447, \cdot)\) n/a 288 2
9792.2.z \(\chi_{9792}(863, \cdot)\) n/a 288 2
9792.2.bb \(\chi_{9792}(1441, \cdot)\) n/a 360 2
9792.2.be \(\chi_{9792}(4033, \cdot)\) n/a 356 2
9792.2.bg \(\chi_{9792}(3455, \cdot)\) n/a 288 2
9792.2.bi \(\chi_{9792}(1871, \cdot)\) n/a 256 2
9792.2.bk \(\chi_{9792}(3025, \cdot)\) n/a 356 2
9792.2.bm \(\chi_{9792}(1585, \cdot)\) n/a 356 2
9792.2.bn \(\chi_{9792}(1007, \cdot)\) n/a 288 2
9792.2.bq \(\chi_{9792}(3263, \cdot)\) n/a 856 2
9792.2.bt \(\chi_{9792}(2209, \cdot)\) n/a 864 2
9792.2.bv \(\chi_{9792}(1055, \cdot)\) n/a 768 2
9792.2.bx \(\chi_{9792}(1631, \cdot)\) n/a 864 2
9792.2.bz \(\chi_{9792}(1633, \cdot)\) n/a 768 2
9792.2.ca \(\chi_{9792}(2687, \cdot)\) n/a 768 2
9792.2.cc \(\chi_{9792}(3841, \cdot)\) n/a 856 2
9792.2.cf \(\chi_{9792}(1511, \cdot)\) None 0 4
9792.2.ch \(\chi_{9792}(3817, \cdot)\) None 0 4
9792.2.cj \(\chi_{9792}(2087, \cdot)\) None 0 4
9792.2.cl \(\chi_{9792}(2665, \cdot)\) None 0 4
9792.2.cn \(\chi_{9792}(3239, \cdot)\) None 0 4
9792.2.cp \(\chi_{9792}(937, \cdot)\) None 0 4
9792.2.cs \(\chi_{9792}(2881, \cdot)\) n/a 712 4
9792.2.ct \(\chi_{9792}(2303, \cdot)\) n/a 576 4
9792.2.cu \(\chi_{9792}(4463, \cdot)\) n/a 576 4
9792.2.cv \(\chi_{9792}(433, \cdot)\) n/a 712 4
9792.2.cy \(\chi_{9792}(1801, \cdot)\) None 0 4
9792.2.cz \(\chi_{9792}(647, \cdot)\) None 0 4
9792.2.dc \(\chi_{9792}(1223, \cdot)\) None 0 4
9792.2.dd \(\chi_{9792}(1225, \cdot)\) None 0 4
9792.2.dg \(\chi_{9792}(1583, \cdot)\) n/a 576 4
9792.2.dh \(\chi_{9792}(145, \cdot)\) n/a 712 4
9792.2.dk \(\chi_{9792}(865, \cdot)\) n/a 720 4
9792.2.dl \(\chi_{9792}(287, \cdot)\) n/a 576 4
9792.2.dp \(\chi_{9792}(2089, \cdot)\) None 0 4
9792.2.dr \(\chi_{9792}(2807, \cdot)\) None 0 4
9792.2.ds \(\chi_{9792}(217, \cdot)\) None 0 4
9792.2.du \(\chi_{9792}(4535, \cdot)\) None 0 4
9792.2.dx \(\chi_{9792}(3385, \cdot)\) None 0 4
9792.2.dz \(\chi_{9792}(359, \cdot)\) None 0 4
9792.2.ea \(\chi_{9792}(1679, \cdot)\) n/a 1712 4
9792.2.ed \(\chi_{9792}(2257, \cdot)\) n/a 1712 4
9792.2.ee \(\chi_{9792}(1393, \cdot)\) n/a 1712 4
9792.2.eg \(\chi_{9792}(239, \cdot)\) n/a 1536 4
9792.2.ej \(\chi_{9792}(769, \cdot)\) n/a 1712 4
9792.2.el \(\chi_{9792}(191, \cdot)\) n/a 1712 4
9792.2.em \(\chi_{9792}(1823, \cdot)\) n/a 1728 4
9792.2.eo \(\chi_{9792}(2401, \cdot)\) n/a 1728 4
9792.2.er \(\chi_{9792}(815, \cdot)\) n/a 1712 4
9792.2.et \(\chi_{9792}(817, \cdot)\) n/a 1536 4
9792.2.eu \(\chi_{9792}(625, \cdot)\) n/a 1712 4
9792.2.ex \(\chi_{9792}(47, \cdot)\) n/a 1712 4
9792.2.fa \(\chi_{9792}(197, \cdot)\) n/a 4608 8
9792.2.fb \(\chi_{9792}(1099, \cdot)\) n/a 5744 8
9792.2.fc \(\chi_{9792}(757, \cdot)\) n/a 5744 8
9792.2.fe \(\chi_{9792}(899, \cdot)\) n/a 4608 8
9792.2.fg \(\chi_{9792}(235, \cdot)\) n/a 5744 8
9792.2.fh \(\chi_{9792}(1421, \cdot)\) n/a 4608 8
9792.2.fl \(\chi_{9792}(2033, \cdot)\) n/a 1152 8
9792.2.fm \(\chi_{9792}(1999, \cdot)\) n/a 1424 8
9792.2.fp \(\chi_{9792}(343, \cdot)\) None 0 8
9792.2.fq \(\chi_{9792}(233, \cdot)\) None 0 8
9792.2.fs \(\chi_{9792}(467, \cdot)\) n/a 4608 8
9792.2.fu \(\chi_{9792}(1477, \cdot)\) n/a 5744 8
9792.2.fy \(\chi_{9792}(413, \cdot)\) n/a 4608 8
9792.2.fz \(\chi_{9792}(1387, \cdot)\) n/a 5744 8
9792.2.gc \(\chi_{9792}(269, \cdot)\) n/a 4608 8
9792.2.gd \(\chi_{9792}(91, \cdot)\) n/a 5744 8
9792.2.ge \(\chi_{9792}(811, \cdot)\) n/a 5744 8
9792.2.gf \(\chi_{9792}(2213, \cdot)\) n/a 4608 8
9792.2.gk \(\chi_{9792}(613, \cdot)\) n/a 5120 8
9792.2.gl \(\chi_{9792}(611, \cdot)\) n/a 4608 8
9792.2.gn \(\chi_{9792}(449, \cdot)\) n/a 1152 8
9792.2.go \(\chi_{9792}(703, \cdot)\) n/a 1424 8
9792.2.gq \(\chi_{9792}(377, \cdot)\) None 0 8
9792.2.gt \(\chi_{9792}(199, \cdot)\) None 0 8
9792.2.gu \(\chi_{9792}(829, \cdot)\) n/a 5744 8
9792.2.gv \(\chi_{9792}(251, \cdot)\) n/a 4608 8
9792.2.ha \(\chi_{9792}(973, \cdot)\) n/a 5744 8
9792.2.hb \(\chi_{9792}(395, \cdot)\) n/a 4608 8
9792.2.hc \(\chi_{9792}(1673, \cdot)\) None 0 8
9792.2.hf \(\chi_{9792}(2215, \cdot)\) None 0 8
9792.2.hh \(\chi_{9792}(415, \cdot)\) n/a 1440 8
9792.2.hi \(\chi_{9792}(737, \cdot)\) n/a 1152 8
9792.2.hk \(\chi_{9792}(35, \cdot)\) n/a 4096 8
9792.2.hl \(\chi_{9792}(1189, \cdot)\) n/a 5744 8
9792.2.ho \(\chi_{9792}(1133, \cdot)\) n/a 4608 8
9792.2.hp \(\chi_{9792}(163, \cdot)\) n/a 5744 8
9792.2.hs \(\chi_{9792}(325, \cdot)\) n/a 5744 8
9792.2.hu \(\chi_{9792}(179, \cdot)\) n/a 4608 8
9792.2.hw \(\chi_{9792}(1639, \cdot)\) None 0 8
9792.2.hz \(\chi_{9792}(2249, \cdot)\) None 0 8
9792.2.ib \(\chi_{9792}(881, \cdot)\) n/a 1152 8
9792.2.ic \(\chi_{9792}(847, \cdot)\) n/a 1424 8
9792.2.ie \(\chi_{9792}(379, \cdot)\) n/a 5744 8
9792.2.if \(\chi_{9792}(125, \cdot)\) n/a 4608 8
9792.2.ii \(\chi_{9792}(1691, \cdot)\) n/a 4608 8
9792.2.ik \(\chi_{9792}(253, \cdot)\) n/a 5744 8
9792.2.io \(\chi_{9792}(2035, \cdot)\) n/a 5744 8
9792.2.ip \(\chi_{9792}(2357, \cdot)\) n/a 4608 8
9792.2.iq \(\chi_{9792}(121, \cdot)\) None 0 8
9792.2.is \(\chi_{9792}(3143, \cdot)\) None 0 8
9792.2.iv \(\chi_{9792}(1271, \cdot)\) None 0 8
9792.2.ix \(\chi_{9792}(1849, \cdot)\) None 0 8
9792.2.iy \(\chi_{9792}(1607, \cdot)\) None 0 8
9792.2.ja \(\chi_{9792}(25, \cdot)\) None 0 8
9792.2.jc \(\chi_{9792}(1249, \cdot)\) n/a 3456 8
9792.2.jd \(\chi_{9792}(671, \cdot)\) n/a 3456 8
9792.2.ji \(\chi_{9792}(1103, \cdot)\) n/a 3424 8
9792.2.jj \(\chi_{9792}(529, \cdot)\) n/a 3424 8
9792.2.jm \(\chi_{9792}(409, \cdot)\) None 0 8
9792.2.jn \(\chi_{9792}(407, \cdot)\) None 0 8
9792.2.jq \(\chi_{9792}(1463, \cdot)\) None 0 8
9792.2.jr \(\chi_{9792}(169, \cdot)\) None 0 8
9792.2.ju \(\chi_{9792}(1487, \cdot)\) n/a 3424 8
9792.2.jv \(\chi_{9792}(49, \cdot)\) n/a 3424 8
9792.2.jy \(\chi_{9792}(961, \cdot)\) n/a 3424 8
9792.2.jz \(\chi_{9792}(383, \cdot)\) n/a 3424 8
9792.2.ka \(\chi_{9792}(457, \cdot)\) None 0 8
9792.2.kc \(\chi_{9792}(263, \cdot)\) None 0 8
9792.2.ke \(\chi_{9792}(1033, \cdot)\) None 0 8
9792.2.kg \(\chi_{9792}(455, \cdot)\) None 0 8
9792.2.ki \(\chi_{9792}(1991, \cdot)\) None 0 8
9792.2.kk \(\chi_{9792}(553, \cdot)\) None 0 8
9792.2.km \(\chi_{9792}(547, \cdot)\) n/a 27584 16
9792.2.kn \(\chi_{9792}(533, \cdot)\) n/a 27584 16
9792.2.kr \(\chi_{9792}(59, \cdot)\) n/a 27584 16
9792.2.kt \(\chi_{9792}(1573, \cdot)\) n/a 27584 16
9792.2.kw \(\chi_{9792}(5, \cdot)\) n/a 27584 16
9792.2.kx \(\chi_{9792}(979, \cdot)\) n/a 27584 16
9792.2.kz \(\chi_{9792}(367, \cdot)\) n/a 6848 16
9792.2.la \(\chi_{9792}(401, \cdot)\) n/a 6848 16
9792.2.lc \(\chi_{9792}(7, \cdot)\) None 0 16
9792.2.lf \(\chi_{9792}(617, \cdot)\) None 0 16
9792.2.lh \(\chi_{9792}(155, \cdot)\) n/a 27584 16
9792.2.lj \(\chi_{9792}(637, \cdot)\) n/a 27584 16
9792.2.lm \(\chi_{9792}(691, \cdot)\) n/a 27584 16
9792.2.ln \(\chi_{9792}(581, \cdot)\) n/a 27584 16
9792.2.lq \(\chi_{9792}(373, \cdot)\) n/a 27584 16
9792.2.lr \(\chi_{9792}(443, \cdot)\) n/a 24576 16
9792.2.lt \(\chi_{9792}(895, \cdot)\) n/a 6848 16
9792.2.lu \(\chi_{9792}(65, \cdot)\) n/a 6848 16
9792.2.lw \(\chi_{9792}(41, \cdot)\) None 0 16
9792.2.lz \(\chi_{9792}(583, \cdot)\) None 0 16
9792.2.ma \(\chi_{9792}(157, \cdot)\) n/a 27584 16
9792.2.mb \(\chi_{9792}(659, \cdot)\) n/a 27584 16
9792.2.mg \(\chi_{9792}(13, \cdot)\) n/a 27584 16
9792.2.mh \(\chi_{9792}(803, \cdot)\) n/a 27584 16
9792.2.mi \(\chi_{9792}(473, \cdot)\) None 0 16
9792.2.ml \(\chi_{9792}(1159, \cdot)\) None 0 16
9792.2.mn \(\chi_{9792}(929, \cdot)\) n/a 6912 16
9792.2.mo \(\chi_{9792}(31, \cdot)\) n/a 6912 16
9792.2.mq \(\chi_{9792}(203, \cdot)\) n/a 27584 16
9792.2.mr \(\chi_{9792}(205, \cdot)\) n/a 24576 16
9792.2.mw \(\chi_{9792}(437, \cdot)\) n/a 27584 16
9792.2.mx \(\chi_{9792}(499, \cdot)\) n/a 27584 16
9792.2.my \(\chi_{9792}(283, \cdot)\) n/a 27584 16
9792.2.mz \(\chi_{9792}(245, \cdot)\) n/a 27584 16
9792.2.nc \(\chi_{9792}(619, \cdot)\) n/a 27584 16
9792.2.nd \(\chi_{9792}(29, \cdot)\) n/a 27584 16
9792.2.nh \(\chi_{9792}(349, \cdot)\) n/a 27584 16
9792.2.nj \(\chi_{9792}(995, \cdot)\) n/a 27584 16
9792.2.nl \(\chi_{9792}(439, \cdot)\) None 0 16
9792.2.nm \(\chi_{9792}(1193, \cdot)\) None 0 16
9792.2.np \(\chi_{9792}(79, \cdot)\) n/a 6848 16
9792.2.nq \(\chi_{9792}(113, \cdot)\) n/a 6848 16
9792.2.nu \(\chi_{9792}(317, \cdot)\) n/a 27584 16
9792.2.nv \(\chi_{9792}(139, \cdot)\) n/a 27584 16
9792.2.nx \(\chi_{9792}(229, \cdot)\) n/a 27584 16
9792.2.nz \(\chi_{9792}(563, \cdot)\) n/a 27584 16
9792.2.oa \(\chi_{9792}(725, \cdot)\) n/a 27584 16
9792.2.ob \(\chi_{9792}(403, \cdot)\) n/a 27584 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9792))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9792)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(306))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(408))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(544))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(612))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(816))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1088))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1632))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2448))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3264))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4896))\)\(^{\oplus 2}\)