Properties

Label 7488.2
Level 7488
Weight 2
Dimension 679086
Nonzero newspaces 140
Sturm bound 6193152

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Defining parameters

Level: \( N \) = \( 7488 = 2^{6} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 140 \)
Sturm bound: \(6193152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7488))\).

Total New Old
Modular forms 1562112 683442 878670
Cusp forms 1534465 679086 855379
Eisenstein series 27647 4356 23291

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7488))\)

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
7488.2.a \(\chi_{7488}(1, \cdot)\) 7488.2.a.a 1 1
7488.2.a.b 1
7488.2.a.c 1
7488.2.a.d 1
7488.2.a.e 1
7488.2.a.f 1
7488.2.a.g 1
7488.2.a.h 1
7488.2.a.i 1
7488.2.a.j 1
7488.2.a.k 1
7488.2.a.l 1
7488.2.a.m 1
7488.2.a.n 1
7488.2.a.o 1
7488.2.a.p 1
7488.2.a.q 1
7488.2.a.r 1
7488.2.a.s 1
7488.2.a.t 1
7488.2.a.u 1
7488.2.a.v 1
7488.2.a.w 1
7488.2.a.x 1
7488.2.a.y 1
7488.2.a.z 1
7488.2.a.ba 1
7488.2.a.bb 1
7488.2.a.bc 1
7488.2.a.bd 1
7488.2.a.be 1
7488.2.a.bf 1
7488.2.a.bg 1
7488.2.a.bh 1
7488.2.a.bi 1
7488.2.a.bj 1
7488.2.a.bk 1
7488.2.a.bl 1
7488.2.a.bm 1
7488.2.a.bn 1
7488.2.a.bo 1
7488.2.a.bp 1
7488.2.a.bq 1
7488.2.a.br 1
7488.2.a.bs 1
7488.2.a.bt 1
7488.2.a.bu 1
7488.2.a.bv 1
7488.2.a.bw 1
7488.2.a.bx 1
7488.2.a.by 1
7488.2.a.bz 1
7488.2.a.ca 1
7488.2.a.cb 1
7488.2.a.cc 1
7488.2.a.cd 1
7488.2.a.ce 2
7488.2.a.cf 2
7488.2.a.cg 2
7488.2.a.ch 2
7488.2.a.ci 2
7488.2.a.cj 2
7488.2.a.ck 2
7488.2.a.cl 2
7488.2.a.cm 2
7488.2.a.cn 2
7488.2.a.co 2
7488.2.a.cp 2
7488.2.a.cq 2
7488.2.a.cr 2
7488.2.a.cs 2
7488.2.a.ct 2
7488.2.a.cu 2
7488.2.a.cv 2
7488.2.a.cw 2
7488.2.a.cx 3
7488.2.a.cy 3
7488.2.a.cz 4
7488.2.a.da 4
7488.2.a.db 4
7488.2.a.dc 4
7488.2.a.dd 4
7488.2.c \(\chi_{7488}(3457, \cdot)\) n/a 138 1
7488.2.d \(\chi_{7488}(4031, \cdot)\) 7488.2.d.a 4 1
7488.2.d.b 4
7488.2.d.c 4
7488.2.d.d 4
7488.2.d.e 4
7488.2.d.f 8
7488.2.d.g 8
7488.2.d.h 8
7488.2.d.i 8
7488.2.d.j 8
7488.2.d.k 12
7488.2.d.l 12
7488.2.d.m 12
7488.2.g \(\chi_{7488}(3745, \cdot)\) n/a 120 1
7488.2.h \(\chi_{7488}(3743, \cdot)\) n/a 112 1
7488.2.j \(\chi_{7488}(287, \cdot)\) 7488.2.j.a 16 1
7488.2.j.b 16
7488.2.j.c 32
7488.2.j.d 32
7488.2.m \(\chi_{7488}(7201, \cdot)\) n/a 140 1
7488.2.n \(\chi_{7488}(7487, \cdot)\) n/a 112 1
7488.2.q \(\chi_{7488}(2497, \cdot)\) n/a 576 2
7488.2.r \(\chi_{7488}(1537, \cdot)\) n/a 664 2
7488.2.s \(\chi_{7488}(6145, \cdot)\) n/a 664 2
7488.2.t \(\chi_{7488}(1153, \cdot)\) n/a 276 2
7488.2.u \(\chi_{7488}(5455, \cdot)\) n/a 276 2
7488.2.x \(\chi_{7488}(593, \cdot)\) n/a 224 2
7488.2.y \(\chi_{7488}(1871, \cdot)\) n/a 224 2
7488.2.ba \(\chi_{7488}(1873, \cdot)\) n/a 240 2
7488.2.be \(\chi_{7488}(5023, \cdot)\) n/a 280 2
7488.2.bf \(\chi_{7488}(1279, \cdot)\) n/a 276 2
7488.2.bi \(\chi_{7488}(3905, \cdot)\) n/a 224 2
7488.2.bj \(\chi_{7488}(161, \cdot)\) n/a 224 2
7488.2.bk \(\chi_{7488}(2159, \cdot)\) n/a 192 2
7488.2.bm \(\chi_{7488}(1585, \cdot)\) n/a 276 2
7488.2.bp \(\chi_{7488}(4337, \cdot)\) n/a 224 2
7488.2.bq \(\chi_{7488}(1711, \cdot)\) n/a 276 2
7488.2.bt \(\chi_{7488}(2591, \cdot)\) n/a 224 2
7488.2.bu \(\chi_{7488}(289, \cdot)\) n/a 280 2
7488.2.bx \(\chi_{7488}(575, \cdot)\) n/a 224 2
7488.2.by \(\chi_{7488}(2305, \cdot)\) n/a 276 2
7488.2.ca \(\chi_{7488}(3553, \cdot)\) n/a 672 2
7488.2.cd \(\chi_{7488}(1823, \cdot)\) n/a 672 2
7488.2.cf \(\chi_{7488}(3839, \cdot)\) n/a 664 2
7488.2.ch \(\chi_{7488}(2495, \cdot)\) n/a 664 2
7488.2.cl \(\chi_{7488}(6431, \cdot)\) n/a 672 2
7488.2.cn \(\chi_{7488}(2209, \cdot)\) n/a 672 2
7488.2.co \(\chi_{7488}(2783, \cdot)\) n/a 576 2
7488.2.cq \(\chi_{7488}(673, \cdot)\) n/a 672 2
7488.2.cu \(\chi_{7488}(959, \cdot)\) n/a 664 2
7488.2.cw \(\chi_{7488}(191, \cdot)\) n/a 664 2
7488.2.cx \(\chi_{7488}(1921, \cdot)\) n/a 664 2
7488.2.cz \(\chi_{7488}(5281, \cdot)\) n/a 672 2
7488.2.db \(\chi_{7488}(1247, \cdot)\) n/a 672 2
7488.2.de \(\chi_{7488}(1249, \cdot)\) n/a 576 2
7488.2.dg \(\chi_{7488}(95, \cdot)\) n/a 672 2
7488.2.dh \(\chi_{7488}(4417, \cdot)\) n/a 664 2
7488.2.dj \(\chi_{7488}(1535, \cdot)\) n/a 576 2
7488.2.dm \(\chi_{7488}(961, \cdot)\) n/a 664 2
7488.2.do \(\chi_{7488}(2687, \cdot)\) n/a 664 2
7488.2.dq \(\chi_{7488}(4703, \cdot)\) n/a 672 2
7488.2.dr \(\chi_{7488}(2401, \cdot)\) n/a 672 2
7488.2.dv \(\chi_{7488}(3455, \cdot)\) n/a 224 2
7488.2.dw \(\chi_{7488}(3169, \cdot)\) n/a 280 2
7488.2.dz \(\chi_{7488}(1439, \cdot)\) n/a 224 2
7488.2.eb \(\chi_{7488}(2969, \cdot)\) None 0 4
7488.2.ed \(\chi_{7488}(343, \cdot)\) None 0 4
7488.2.ee \(\chi_{7488}(649, \cdot)\) None 0 4
7488.2.eg \(\chi_{7488}(937, \cdot)\) None 0 4
7488.2.ej \(\chi_{7488}(1223, \cdot)\) None 0 4
7488.2.el \(\chi_{7488}(935, \cdot)\) None 0 4
7488.2.em \(\chi_{7488}(1097, \cdot)\) None 0 4
7488.2.eo \(\chi_{7488}(2215, \cdot)\) None 0 4
7488.2.eq \(\chi_{7488}(305, \cdot)\) n/a 448 4
7488.2.et \(\chi_{7488}(271, \cdot)\) n/a 552 4
7488.2.eu \(\chi_{7488}(1553, \cdot)\) n/a 1328 4
7488.2.ew \(\chi_{7488}(655, \cdot)\) n/a 1328 4
7488.2.ey \(\chi_{7488}(943, \cdot)\) n/a 1328 4
7488.2.fb \(\chi_{7488}(977, \cdot)\) n/a 1328 4
7488.2.fd \(\chi_{7488}(785, \cdot)\) n/a 1328 4
7488.2.ff \(\chi_{7488}(1519, \cdot)\) n/a 1328 4
7488.2.fg \(\chi_{7488}(529, \cdot)\) n/a 1328 4
7488.2.fi \(\chi_{7488}(2831, \cdot)\) n/a 1328 4
7488.2.fl \(\chi_{7488}(911, \cdot)\) n/a 1152 4
7488.2.fo \(\chi_{7488}(433, \cdot)\) n/a 552 4
7488.2.fp \(\chi_{7488}(2545, \cdot)\) n/a 1328 4
7488.2.fs \(\chi_{7488}(2447, \cdot)\) n/a 448 4
7488.2.ft \(\chi_{7488}(815, \cdot)\) n/a 1328 4
7488.2.fv \(\chi_{7488}(337, \cdot)\) n/a 1328 4
7488.2.fw \(\chi_{7488}(1087, \cdot)\) n/a 1328 4
7488.2.fx \(\chi_{7488}(31, \cdot)\) n/a 1344 4
7488.2.gc \(\chi_{7488}(4193, \cdot)\) n/a 448 4
7488.2.gd \(\chi_{7488}(449, \cdot)\) n/a 448 4
7488.2.ge \(\chi_{7488}(3521, \cdot)\) n/a 1328 4
7488.2.gf \(\chi_{7488}(353, \cdot)\) n/a 1344 4
7488.2.gk \(\chi_{7488}(929, \cdot)\) n/a 1344 4
7488.2.gl \(\chi_{7488}(2945, \cdot)\) n/a 1328 4
7488.2.go \(\chi_{7488}(5311, \cdot)\) n/a 552 4
7488.2.gp \(\chi_{7488}(1567, \cdot)\) n/a 560 4
7488.2.gq \(\chi_{7488}(223, \cdot)\) n/a 1344 4
7488.2.gr \(\chi_{7488}(319, \cdot)\) n/a 1328 4
7488.2.gw \(\chi_{7488}(895, \cdot)\) n/a 1328 4
7488.2.gx \(\chi_{7488}(799, \cdot)\) n/a 1344 4
7488.2.gy \(\chi_{7488}(2657, \cdot)\) n/a 1344 4
7488.2.gz \(\chi_{7488}(1217, \cdot)\) n/a 1328 4
7488.2.hd \(\chi_{7488}(623, \cdot)\) n/a 1328 4
7488.2.hg \(\chi_{7488}(2161, \cdot)\) n/a 552 4
7488.2.hh \(\chi_{7488}(1777, \cdot)\) n/a 1328 4
7488.2.hk \(\chi_{7488}(719, \cdot)\) n/a 448 4
7488.2.hl \(\chi_{7488}(335, \cdot)\) n/a 1328 4
7488.2.hn \(\chi_{7488}(625, \cdot)\) n/a 1152 4
7488.2.ho \(\chi_{7488}(49, \cdot)\) n/a 1328 4
7488.2.hq \(\chi_{7488}(2063, \cdot)\) n/a 1328 4
7488.2.ht \(\chi_{7488}(175, \cdot)\) n/a 1328 4
7488.2.hv \(\chi_{7488}(401, \cdot)\) n/a 1328 4
7488.2.hx \(\chi_{7488}(3089, \cdot)\) n/a 1328 4
7488.2.hy \(\chi_{7488}(463, \cdot)\) n/a 1328 4
7488.2.ia \(\chi_{7488}(2671, \cdot)\) n/a 1328 4
7488.2.ic \(\chi_{7488}(2225, \cdot)\) n/a 1328 4
7488.2.if \(\chi_{7488}(847, \cdot)\) n/a 552 4
7488.2.ig \(\chi_{7488}(3473, \cdot)\) n/a 448 4
7488.2.ii \(\chi_{7488}(469, \cdot)\) n/a 3840 8
7488.2.ij \(\chi_{7488}(467, \cdot)\) n/a 3584 8
7488.2.im \(\chi_{7488}(125, \cdot)\) n/a 3584 8
7488.2.in \(\chi_{7488}(307, \cdot)\) n/a 4464 8
7488.2.iq \(\chi_{7488}(1061, \cdot)\) n/a 3584 8
7488.2.ir \(\chi_{7488}(1243, \cdot)\) n/a 4464 8
7488.2.iu \(\chi_{7488}(755, \cdot)\) n/a 3072 8
7488.2.iv \(\chi_{7488}(181, \cdot)\) n/a 4464 8
7488.2.iz \(\chi_{7488}(7, \cdot)\) None 0 8
7488.2.jb \(\chi_{7488}(137, \cdot)\) None 0 8
7488.2.jd \(\chi_{7488}(281, \cdot)\) None 0 8
7488.2.jg \(\chi_{7488}(1159, \cdot)\) None 0 8
7488.2.jh \(\chi_{7488}(487, \cdot)\) None 0 8
7488.2.jk \(\chi_{7488}(89, \cdot)\) None 0 8
7488.2.jl \(\chi_{7488}(617, \cdot)\) None 0 8
7488.2.jn \(\chi_{7488}(151, \cdot)\) None 0 8
7488.2.jp \(\chi_{7488}(313, \cdot)\) None 0 8
7488.2.jr \(\chi_{7488}(25, \cdot)\) None 0 8
7488.2.jt \(\chi_{7488}(503, \cdot)\) None 0 8
7488.2.ju \(\chi_{7488}(23, \cdot)\) None 0 8
7488.2.jw \(\chi_{7488}(1031, \cdot)\) None 0 8
7488.2.jy \(\chi_{7488}(887, \cdot)\) None 0 8
7488.2.ka \(\chi_{7488}(263, \cdot)\) None 0 8
7488.2.kd \(\chi_{7488}(647, \cdot)\) None 0 8
7488.2.ke \(\chi_{7488}(361, \cdot)\) None 0 8
7488.2.kh \(\chi_{7488}(1465, \cdot)\) None 0 8
7488.2.kj \(\chi_{7488}(601, \cdot)\) None 0 8
7488.2.kl \(\chi_{7488}(745, \cdot)\) None 0 8
7488.2.kn \(\chi_{7488}(121, \cdot)\) None 0 8
7488.2.ko \(\chi_{7488}(217, \cdot)\) None 0 8
7488.2.kq \(\chi_{7488}(311, \cdot)\) None 0 8
7488.2.ks \(\chi_{7488}(599, \cdot)\) None 0 8
7488.2.ku \(\chi_{7488}(473, \cdot)\) None 0 8
7488.2.kw \(\chi_{7488}(583, \cdot)\) None 0 8
7488.2.kx \(\chi_{7488}(1783, \cdot)\) None 0 8
7488.2.la \(\chi_{7488}(665, \cdot)\) None 0 8
7488.2.lb \(\chi_{7488}(713, \cdot)\) None 0 8
7488.2.le \(\chi_{7488}(1591, \cdot)\) None 0 8
7488.2.lg \(\chi_{7488}(1735, \cdot)\) None 0 8
7488.2.li \(\chi_{7488}(41, \cdot)\) None 0 8
7488.2.lm \(\chi_{7488}(179, \cdot)\) n/a 7168 16
7488.2.ln \(\chi_{7488}(685, \cdot)\) n/a 8928 16
7488.2.lo \(\chi_{7488}(205, \cdot)\) n/a 21440 16
7488.2.lp \(\chi_{7488}(347, \cdot)\) n/a 21440 16
7488.2.lu \(\chi_{7488}(419, \cdot)\) n/a 21440 16
7488.2.lv \(\chi_{7488}(493, \cdot)\) n/a 21440 16
7488.2.lw \(\chi_{7488}(131, \cdot)\) n/a 18432 16
7488.2.lx \(\chi_{7488}(277, \cdot)\) n/a 21440 16
7488.2.mc \(\chi_{7488}(163, \cdot)\) n/a 8928 16
7488.2.md \(\chi_{7488}(197, \cdot)\) n/a 7168 16
7488.2.me \(\chi_{7488}(643, \cdot)\) n/a 21440 16
7488.2.mf \(\chi_{7488}(245, \cdot)\) n/a 21440 16
7488.2.mk \(\chi_{7488}(317, \cdot)\) n/a 21440 16
7488.2.ml \(\chi_{7488}(67, \cdot)\) n/a 21440 16
7488.2.mm \(\chi_{7488}(461, \cdot)\) n/a 21440 16
7488.2.mn \(\chi_{7488}(499, \cdot)\) n/a 21440 16
7488.2.mq \(\chi_{7488}(115, \cdot)\) n/a 21440 16
7488.2.mr \(\chi_{7488}(149, \cdot)\) n/a 21440 16
7488.2.mw \(\chi_{7488}(5, \cdot)\) n/a 21440 16
7488.2.mx \(\chi_{7488}(331, \cdot)\) n/a 21440 16
7488.2.my \(\chi_{7488}(605, \cdot)\) n/a 21440 16
7488.2.mz \(\chi_{7488}(187, \cdot)\) n/a 21440 16
7488.2.ne \(\chi_{7488}(19, \cdot)\) n/a 8928 16
7488.2.nf \(\chi_{7488}(917, \cdot)\) n/a 7168 16
7488.2.ng \(\chi_{7488}(563, \cdot)\) n/a 21440 16
7488.2.nh \(\chi_{7488}(133, \cdot)\) n/a 21440 16
7488.2.nm \(\chi_{7488}(61, \cdot)\) n/a 21440 16
7488.2.nn \(\chi_{7488}(155, \cdot)\) n/a 21440 16
7488.2.no \(\chi_{7488}(157, \cdot)\) n/a 18432 16
7488.2.np \(\chi_{7488}(491, \cdot)\) n/a 21440 16
7488.2.nu \(\chi_{7488}(829, \cdot)\) n/a 8928 16
7488.2.nv \(\chi_{7488}(35, \cdot)\) n/a 7168 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7488))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7488)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(468))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(624))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(832))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(936))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1248))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1872))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2496))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3744))\)\(^{\oplus 2}\)