# Properties

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

## 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

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