# Properties

 Label 7623.2 Level 7623 Weight 2 Dimension 1553877 Nonzero newspaces 80 Sturm bound 8363520

## Defining parameters

 Level: $$N$$ = $$7623 = 3^{2} \cdot 7 \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$80$$ Sturm bound: $$8363520$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(7623))$$.

Total New Old
Modular forms 2106240 1566521 539719
Cusp forms 2075521 1553877 521644
Eisenstein series 30719 12644 18075

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(7623))$$

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
7623.2.a $$\chi_{7623}(1, \cdot)$$ 7623.2.a.a 1 1
7623.2.a.b 1
7623.2.a.c 1
7623.2.a.d 1
7623.2.a.e 1
7623.2.a.f 1
7623.2.a.g 1
7623.2.a.h 1
7623.2.a.i 1
7623.2.a.j 1
7623.2.a.k 1
7623.2.a.l 1
7623.2.a.m 1
7623.2.a.n 1
7623.2.a.o 1
7623.2.a.p 1
7623.2.a.q 1
7623.2.a.r 1
7623.2.a.s 1
7623.2.a.t 2
7623.2.a.u 2
7623.2.a.v 2
7623.2.a.w 2
7623.2.a.x 2
7623.2.a.y 2
7623.2.a.z 2
7623.2.a.ba 2
7623.2.a.bb 2
7623.2.a.bc 2
7623.2.a.bd 2
7623.2.a.be 2
7623.2.a.bf 2
7623.2.a.bg 2
7623.2.a.bh 2
7623.2.a.bi 2
7623.2.a.bj 2
7623.2.a.bk 2
7623.2.a.bl 2
7623.2.a.bm 2
7623.2.a.bn 2
7623.2.a.bo 2
7623.2.a.bp 2
7623.2.a.bq 2
7623.2.a.br 2
7623.2.a.bs 2
7623.2.a.bt 2
7623.2.a.bu 2
7623.2.a.bv 2
7623.2.a.bw 2
7623.2.a.bx 2
7623.2.a.by 2
7623.2.a.bz 3
7623.2.a.ca 3
7623.2.a.cb 3
7623.2.a.cc 3
7623.2.a.cd 3
7623.2.a.ce 3
7623.2.a.cf 4
7623.2.a.cg 4
7623.2.a.ch 4
7623.2.a.ci 4
7623.2.a.cj 4
7623.2.a.ck 4
7623.2.a.cl 4
7623.2.a.cm 4
7623.2.a.cn 4
7623.2.a.co 4
7623.2.a.cp 6
7623.2.a.cq 6
7623.2.a.cr 6
7623.2.a.cs 6
7623.2.a.ct 8
7623.2.a.cu 8
7623.2.a.cv 8
7623.2.a.cw 8
7623.2.a.cx 10
7623.2.a.cy 10
7623.2.a.cz 12
7623.2.a.da 12
7623.2.a.db 16
7623.2.a.dc 16
7623.2.c $$\chi_{7623}(1693, \cdot)$$ n/a 352 1
7623.2.e $$\chi_{7623}(1574, \cdot)$$ n/a 292 1
7623.2.g $$\chi_{7623}(4355, \cdot)$$ n/a 216 1
7623.2.i $$\chi_{7623}(2179, \cdot)$$ n/a 708 2
7623.2.j $$\chi_{7623}(2542, \cdot)$$ n/a 1308 2
7623.2.k $$\chi_{7623}(1453, \cdot)$$ n/a 1708 2
7623.2.l $$\chi_{7623}(3994, \cdot)$$ n/a 1708 2
7623.2.m $$\chi_{7623}(1576, \cdot)$$ n/a 1080 4
7623.2.n $$\chi_{7623}(4478, \cdot)$$ n/a 1708 2
7623.2.p $$\chi_{7623}(241, \cdot)$$ n/a 1696 2
7623.2.r $$\chi_{7623}(725, \cdot)$$ n/a 1696 2
7623.2.w $$\chi_{7623}(1814, \cdot)$$ n/a 1296 2
7623.2.x $$\chi_{7623}(3266, \cdot)$$ n/a 576 2
7623.2.ba $$\chi_{7623}(4597, \cdot)$$ n/a 1696 2
7623.2.bd $$\chi_{7623}(4115, \cdot)$$ n/a 1708 2
7623.2.be $$\chi_{7623}(2663, \cdot)$$ n/a 580 2
7623.2.bg $$\chi_{7623}(2782, \cdot)$$ n/a 704 2
7623.2.bj $$\chi_{7623}(4234, \cdot)$$ n/a 1696 2
7623.2.bk $$\chi_{7623}(122, \cdot)$$ n/a 1708 2
7623.2.bn $$\chi_{7623}(3992, \cdot)$$ n/a 1696 2
7623.2.bq $$\chi_{7623}(2339, \cdot)$$ n/a 864 4
7623.2.bs $$\chi_{7623}(251, \cdot)$$ n/a 1152 4
7623.2.bu $$\chi_{7623}(118, \cdot)$$ n/a 1408 4
7623.2.bw $$\chi_{7623}(694, \cdot)$$ n/a 3300 10
7623.2.bx $$\chi_{7623}(1600, \cdot)$$ n/a 6784 8
7623.2.by $$\chi_{7623}(130, \cdot)$$ n/a 6784 8
7623.2.bz $$\chi_{7623}(487, \cdot)$$ n/a 2816 8
7623.2.ca $$\chi_{7623}(148, \cdot)$$ n/a 5184 8
7623.2.cc $$\chi_{7623}(197, \cdot)$$ n/a 2640 10
7623.2.ce $$\chi_{7623}(188, \cdot)$$ n/a 3520 10
7623.2.cg $$\chi_{7623}(307, \cdot)$$ n/a 4380 10
7623.2.cj $$\chi_{7623}(578, \cdot)$$ n/a 6784 8
7623.2.cm $$\chi_{7623}(614, \cdot)$$ n/a 6784 8
7623.2.co $$\chi_{7623}(766, \cdot)$$ n/a 2816 8
7623.2.cp $$\chi_{7623}(475, \cdot)$$ n/a 6784 8
7623.2.cr $$\chi_{7623}(608, \cdot)$$ n/a 6784 8
7623.2.cu $$\chi_{7623}(269, \cdot)$$ n/a 2304 8
7623.2.cw $$\chi_{7623}(94, \cdot)$$ n/a 6784 8
7623.2.cy $$\chi_{7623}(239, \cdot)$$ n/a 5184 8
7623.2.db $$\chi_{7623}(233, \cdot)$$ n/a 2304 8
7623.2.df $$\chi_{7623}(2048, \cdot)$$ n/a 6784 8
7623.2.dh $$\chi_{7623}(40, \cdot)$$ n/a 6784 8
7623.2.dj $$\chi_{7623}(2084, \cdot)$$ n/a 6784 8
7623.2.dk $$\chi_{7623}(529, \cdot)$$ n/a 21040 20
7623.2.dl $$\chi_{7623}(67, \cdot)$$ n/a 21040 20
7623.2.dm $$\chi_{7623}(232, \cdot)$$ n/a 15840 20
7623.2.dn $$\chi_{7623}(100, \cdot)$$ n/a 8760 20
7623.2.do $$\chi_{7623}(64, \cdot)$$ n/a 13200 40
7623.2.dq $$\chi_{7623}(263, \cdot)$$ n/a 21040 20
7623.2.dt $$\chi_{7623}(551, \cdot)$$ n/a 21040 20
7623.2.du $$\chi_{7623}(76, \cdot)$$ n/a 21040 20
7623.2.dx $$\chi_{7623}(10, \cdot)$$ n/a 8760 20
7623.2.dz $$\chi_{7623}(89, \cdot)$$ n/a 7040 20
7623.2.ea $$\chi_{7623}(419, \cdot)$$ n/a 21040 20
7623.2.ed $$\chi_{7623}(439, \cdot)$$ n/a 21040 20
7623.2.eg $$\chi_{7623}(296, \cdot)$$ n/a 7040 20
7623.2.eh $$\chi_{7623}(428, \cdot)$$ n/a 15840 20
7623.2.em $$\chi_{7623}(32, \cdot)$$ n/a 21040 20
7623.2.eo $$\chi_{7623}(670, \cdot)$$ n/a 21040 20
7623.2.eq $$\chi_{7623}(320, \cdot)$$ n/a 21040 20
7623.2.es $$\chi_{7623}(244, \cdot)$$ n/a 17520 40
7623.2.eu $$\chi_{7623}(125, \cdot)$$ n/a 14080 40
7623.2.ew $$\chi_{7623}(8, \cdot)$$ n/a 10560 40
7623.2.ey $$\chi_{7623}(169, \cdot)$$ n/a 63360 80
7623.2.ez $$\chi_{7623}(37, \cdot)$$ n/a 35040 80
7623.2.fa $$\chi_{7623}(4, \cdot)$$ n/a 84160 80
7623.2.fb $$\chi_{7623}(25, \cdot)$$ n/a 84160 80
7623.2.fc $$\chi_{7623}(5, \cdot)$$ n/a 84160 80
7623.2.fe $$\chi_{7623}(52, \cdot)$$ n/a 84160 80
7623.2.fg $$\chi_{7623}(2, \cdot)$$ n/a 84160 80
7623.2.fk $$\chi_{7623}(107, \cdot)$$ n/a 28160 80
7623.2.fn $$\chi_{7623}(29, \cdot)$$ n/a 63360 80
7623.2.fp $$\chi_{7623}(61, \cdot)$$ n/a 84160 80
7623.2.fr $$\chi_{7623}(26, \cdot)$$ n/a 28160 80
7623.2.fu $$\chi_{7623}(20, \cdot)$$ n/a 84160 80
7623.2.fw $$\chi_{7623}(13, \cdot)$$ n/a 84160 80
7623.2.fx $$\chi_{7623}(19, \cdot)$$ n/a 35040 80
7623.2.fz $$\chi_{7623}(47, \cdot)$$ n/a 84160 80
7623.2.gc $$\chi_{7623}(74, \cdot)$$ n/a 84160 80

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(7623))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(7623)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(363))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(693))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(847))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1089))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2541))$$$$^{\oplus 2}$$