# Properties

 Label 8624.2 Level 8624 Weight 2 Dimension 1194539 Nonzero newspaces 64 Sturm bound 9031680

## Defining parameters

 Level: $$N$$ = $$8624 = 2^{4} \cdot 7^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$64$$ Sturm bound: $$9031680$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8624))$$.

Total New Old
Modular forms 2274720 1202395 1072325
Cusp forms 2241121 1194539 1046582
Eisenstein series 33599 7856 25743

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8624))$$

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
8624.2.a $$\chi_{8624}(1, \cdot)$$ 8624.2.a.a 1 1
8624.2.a.b 1
8624.2.a.c 1
8624.2.a.d 1
8624.2.a.e 1
8624.2.a.f 1
8624.2.a.g 1
8624.2.a.h 1
8624.2.a.i 1
8624.2.a.j 1
8624.2.a.k 1
8624.2.a.l 1
8624.2.a.m 1
8624.2.a.n 1
8624.2.a.o 1
8624.2.a.p 1
8624.2.a.q 1
8624.2.a.r 1
8624.2.a.s 1
8624.2.a.t 1
8624.2.a.u 1
8624.2.a.v 1
8624.2.a.w 1
8624.2.a.x 1
8624.2.a.y 1
8624.2.a.z 1
8624.2.a.ba 1
8624.2.a.bb 1
8624.2.a.bc 1
8624.2.a.bd 1
8624.2.a.be 1
8624.2.a.bf 2
8624.2.a.bg 2
8624.2.a.bh 2
8624.2.a.bi 2
8624.2.a.bj 2
8624.2.a.bk 2
8624.2.a.bl 2
8624.2.a.bm 2
8624.2.a.bn 2
8624.2.a.bo 2
8624.2.a.bp 2
8624.2.a.bq 2
8624.2.a.br 2
8624.2.a.bs 2
8624.2.a.bt 2
8624.2.a.bu 2
8624.2.a.bv 2
8624.2.a.bw 2
8624.2.a.bx 2
8624.2.a.by 2
8624.2.a.bz 2
8624.2.a.ca 2
8624.2.a.cb 2
8624.2.a.cc 2
8624.2.a.cd 2
8624.2.a.ce 2
8624.2.a.cf 3
8624.2.a.cg 3
8624.2.a.ch 3
8624.2.a.ci 3
8624.2.a.cj 3
8624.2.a.ck 3
8624.2.a.cl 3
8624.2.a.cm 3
8624.2.a.cn 3
8624.2.a.co 3
8624.2.a.cp 3
8624.2.a.cq 3
8624.2.a.cr 4
8624.2.a.cs 4
8624.2.a.ct 4
8624.2.a.cu 4
8624.2.a.cv 4
8624.2.a.cw 4
8624.2.a.cx 4
8624.2.a.cy 4
8624.2.a.cz 4
8624.2.a.da 5
8624.2.a.db 5
8624.2.a.dc 5
8624.2.a.dd 5
8624.2.a.de 8
8624.2.a.df 10
8624.2.a.dg 12
8624.2.c $$\chi_{8624}(4313, \cdot)$$ None 0 1
8624.2.e $$\chi_{8624}(3233, \cdot)$$ n/a 236 1
8624.2.f $$\chi_{8624}(7743, \cdot)$$ n/a 246 1
8624.2.h $$\chi_{8624}(1959, \cdot)$$ None 0 1
8624.2.j $$\chi_{8624}(6271, \cdot)$$ n/a 200 1
8624.2.l $$\chi_{8624}(3431, \cdot)$$ None 0 1
8624.2.o $$\chi_{8624}(7545, \cdot)$$ None 0 1
8624.2.q $$\chi_{8624}(177, \cdot)$$ n/a 400 2
8624.2.r $$\chi_{8624}(1275, \cdot)$$ n/a 1948 2
8624.2.s $$\chi_{8624}(4115, \cdot)$$ n/a 1600 2
8624.2.x $$\chi_{8624}(1077, \cdot)$$ n/a 1904 2
8624.2.y $$\chi_{8624}(2157, \cdot)$$ n/a 1640 2
8624.2.z $$\chi_{8624}(785, \cdot)$$ n/a 964 4
8624.2.ba $$\chi_{8624}(2089, \cdot)$$ None 0 2
8624.2.be $$\chi_{8624}(815, \cdot)$$ n/a 400 2
8624.2.bg $$\chi_{8624}(263, \cdot)$$ None 0 2
8624.2.bi $$\chi_{8624}(4575, \cdot)$$ n/a 480 2
8624.2.bk $$\chi_{8624}(1783, \cdot)$$ None 0 2
8624.2.bl $$\chi_{8624}(1145, \cdot)$$ None 0 2
8624.2.bn $$\chi_{8624}(3057, \cdot)$$ n/a 472 2
8624.2.bp $$\chi_{8624}(1233, \cdot)$$ n/a 1680 6
8624.2.br $$\chi_{8624}(1273, \cdot)$$ None 0 4
8624.2.bu $$\chi_{8624}(2647, \cdot)$$ None 0 4
8624.2.bw $$\chi_{8624}(1567, \cdot)$$ n/a 960 4
8624.2.by $$\chi_{8624}(1175, \cdot)$$ None 0 4
8624.2.ca $$\chi_{8624}(1471, \cdot)$$ n/a 984 4
8624.2.cb $$\chi_{8624}(2449, \cdot)$$ n/a 944 4
8624.2.cd $$\chi_{8624}(1961, \cdot)$$ None 0 4
8624.2.ch $$\chi_{8624}(2971, \cdot)$$ n/a 3200 4
8624.2.ci $$\chi_{8624}(1451, \cdot)$$ n/a 3808 4
8624.2.cj $$\chi_{8624}(2333, \cdot)$$ n/a 3200 4
8624.2.ck $$\chi_{8624}(901, \cdot)$$ n/a 3808 4
8624.2.co $$\chi_{8624}(153, \cdot)$$ None 0 6
8624.2.cr $$\chi_{8624}(967, \cdot)$$ None 0 6
8624.2.ct $$\chi_{8624}(111, \cdot)$$ n/a 1680 6
8624.2.cv $$\chi_{8624}(727, \cdot)$$ None 0 6
8624.2.cx $$\chi_{8624}(351, \cdot)$$ n/a 2016 6
8624.2.cy $$\chi_{8624}(769, \cdot)$$ n/a 2004 6
8624.2.da $$\chi_{8624}(617, \cdot)$$ None 0 6
8624.2.dc $$\chi_{8624}(753, \cdot)$$ n/a 1888 8
8624.2.dd $$\chi_{8624}(1373, \cdot)$$ n/a 7792 8
8624.2.de $$\chi_{8624}(293, \cdot)$$ n/a 7616 8
8624.2.dj $$\chi_{8624}(587, \cdot)$$ n/a 7616 8
8624.2.dk $$\chi_{8624}(491, \cdot)$$ n/a 7792 8
8624.2.dl $$\chi_{8624}(529, \cdot)$$ n/a 3360 12
8624.2.dm $$\chi_{8624}(461, \cdot)$$ n/a 16080 12
8624.2.dn $$\chi_{8624}(309, \cdot)$$ n/a 13440 12
8624.2.ds $$\chi_{8624}(43, \cdot)$$ n/a 16080 12
8624.2.dt $$\chi_{8624}(419, \cdot)$$ n/a 13440 12
8624.2.dv $$\chi_{8624}(129, \cdot)$$ n/a 1888 8
8624.2.dx $$\chi_{8624}(361, \cdot)$$ None 0 8
8624.2.dy $$\chi_{8624}(423, \cdot)$$ None 0 8
8624.2.ea $$\chi_{8624}(79, \cdot)$$ n/a 1920 8
8624.2.ec $$\chi_{8624}(1047, \cdot)$$ None 0 8
8624.2.ee $$\chi_{8624}(31, \cdot)$$ n/a 1920 8
8624.2.ei $$\chi_{8624}(1097, \cdot)$$ None 0 8
8624.2.ej $$\chi_{8624}(113, \cdot)$$ n/a 8016 24
8624.2.el $$\chi_{8624}(241, \cdot)$$ n/a 4008 12
8624.2.en $$\chi_{8624}(793, \cdot)$$ None 0 12
8624.2.eo $$\chi_{8624}(199, \cdot)$$ None 0 12
8624.2.eq $$\chi_{8624}(527, \cdot)$$ n/a 4032 12
8624.2.es $$\chi_{8624}(1143, \cdot)$$ None 0 12
8624.2.eu $$\chi_{8624}(1167, \cdot)$$ n/a 3360 12
8624.2.ey $$\chi_{8624}(857, \cdot)$$ None 0 12
8624.2.fb $$\chi_{8624}(117, \cdot)$$ n/a 15232 16
8624.2.fc $$\chi_{8624}(949, \cdot)$$ n/a 15232 16
8624.2.fd $$\chi_{8624}(459, \cdot)$$ n/a 15232 16
8624.2.fe $$\chi_{8624}(411, \cdot)$$ n/a 15232 16
8624.2.fi $$\chi_{8624}(169, \cdot)$$ None 0 24
8624.2.fk $$\chi_{8624}(321, \cdot)$$ n/a 8016 24
8624.2.fl $$\chi_{8624}(127, \cdot)$$ n/a 8064 24
8624.2.fn $$\chi_{8624}(279, \cdot)$$ None 0 24
8624.2.fp $$\chi_{8624}(223, \cdot)$$ n/a 8064 24
8624.2.fr $$\chi_{8624}(183, \cdot)$$ None 0 24
8624.2.fu $$\chi_{8624}(41, \cdot)$$ None 0 24
8624.2.fy $$\chi_{8624}(221, \cdot)$$ n/a 26880 24
8624.2.fz $$\chi_{8624}(285, \cdot)$$ n/a 32160 24
8624.2.ga $$\chi_{8624}(243, \cdot)$$ n/a 26880 24
8624.2.gb $$\chi_{8624}(219, \cdot)$$ n/a 32160 24
8624.2.ge $$\chi_{8624}(81, \cdot)$$ n/a 16032 48
8624.2.gf $$\chi_{8624}(27, \cdot)$$ n/a 64320 48
8624.2.gg $$\chi_{8624}(211, \cdot)$$ n/a 64320 48
8624.2.gl $$\chi_{8624}(141, \cdot)$$ n/a 64320 48
8624.2.gm $$\chi_{8624}(13, \cdot)$$ n/a 64320 48
8624.2.gn $$\chi_{8624}(73, \cdot)$$ None 0 48
8624.2.gr $$\chi_{8624}(47, \cdot)$$ n/a 16128 48
8624.2.gt $$\chi_{8624}(39, \cdot)$$ None 0 48
8624.2.gv $$\chi_{8624}(95, \cdot)$$ n/a 16128 48
8624.2.gx $$\chi_{8624}(103, \cdot)$$ None 0 48
8624.2.gy $$\chi_{8624}(9, \cdot)$$ None 0 48
8624.2.ha $$\chi_{8624}(17, \cdot)$$ n/a 16032 48
8624.2.he $$\chi_{8624}(51, \cdot)$$ n/a 128640 96
8624.2.hf $$\chi_{8624}(3, \cdot)$$ n/a 128640 96
8624.2.hg $$\chi_{8624}(61, \cdot)$$ n/a 128640 96
8624.2.hh $$\chi_{8624}(37, \cdot)$$ n/a 128640 96

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8624))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8624)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(176))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(308))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(392))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(539))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(616))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(784))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1078))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1232))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2156))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4312))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8624))$$$$^{\oplus 1}$$