# Properties

 Label 9464.2 Level 9464 Weight 2 Dimension 1447860 Nonzero newspaces 90 Sturm bound 10902528

## Defining parameters

 Level: $$N$$ = $$9464 = 2^{3} \cdot 7 \cdot 13^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$90$$ Sturm bound: $$10902528$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(9464))$$.

Total New Old
Modular forms 2742048 1456040 1286008
Cusp forms 2709217 1447860 1261357
Eisenstein series 32831 8180 24651

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(9464))$$

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
9464.2.a $$\chi_{9464}(1, \cdot)$$ 9464.2.a.a 1 1
9464.2.a.b 1
9464.2.a.c 1
9464.2.a.d 1
9464.2.a.e 1
9464.2.a.f 1
9464.2.a.g 1
9464.2.a.h 1
9464.2.a.i 2
9464.2.a.j 2
9464.2.a.k 2
9464.2.a.l 2
9464.2.a.m 2
9464.2.a.n 2
9464.2.a.o 2
9464.2.a.p 2
9464.2.a.q 2
9464.2.a.r 2
9464.2.a.s 2
9464.2.a.t 3
9464.2.a.u 3
9464.2.a.v 4
9464.2.a.w 4
9464.2.a.x 4
9464.2.a.y 4
9464.2.a.z 4
9464.2.a.ba 4
9464.2.a.bb 4
9464.2.a.bc 4
9464.2.a.bd 6
9464.2.a.be 6
9464.2.a.bf 6
9464.2.a.bg 6
9464.2.a.bh 7
9464.2.a.bi 7
9464.2.a.bj 12
9464.2.a.bk 12
9464.2.a.bl 12
9464.2.a.bm 12
9464.2.a.bn 12
9464.2.a.bo 12
9464.2.a.bp 12
9464.2.a.bq 12
9464.2.a.br 15
9464.2.a.bs 15
9464.2.b $$\chi_{9464}(4731, \cdot)$$ n/a 1212 1
9464.2.c $$\chi_{9464}(4733, \cdot)$$ n/a 930 1
9464.2.h $$\chi_{9464}(4395, \cdot)$$ n/a 1218 1
9464.2.i $$\chi_{9464}(5069, \cdot)$$ n/a 924 1
9464.2.j $$\chi_{9464}(9127, \cdot)$$ None 0 1
9464.2.k $$\chi_{9464}(337, \cdot)$$ n/a 232 1
9464.2.p $$\chi_{9464}(9463, \cdot)$$ None 0 1
9464.2.q $$\chi_{9464}(529, \cdot)$$ n/a 616 2
9464.2.r $$\chi_{9464}(1353, \cdot)$$ n/a 620 2
9464.2.s $$\chi_{9464}(4033, \cdot)$$ n/a 460 2
9464.2.t $$\chi_{9464}(7289, \cdot)$$ n/a 616 2
9464.2.v $$\chi_{9464}(239, \cdot)$$ None 0 2
9464.2.w $$\chi_{9464}(4633, \cdot)$$ n/a 616 2
9464.2.z $$\chi_{9464}(99, \cdot)$$ n/a 1848 2
9464.2.ba $$\chi_{9464}(4493, \cdot)$$ n/a 2424 2
9464.2.be $$\chi_{9464}(485, \cdot)$$ n/a 2424 2
9464.2.bf $$\chi_{9464}(4371, \cdot)$$ n/a 2424 2
9464.2.bg $$\chi_{9464}(2557, \cdot)$$ n/a 2424 2
9464.2.bh $$\chi_{9464}(6107, \cdot)$$ n/a 2424 2
9464.2.bm $$\chi_{9464}(3865, \cdot)$$ n/a 464 2
9464.2.bn $$\chi_{9464}(3695, \cdot)$$ None 0 2
9464.2.bo $$\chi_{9464}(4079, \cdot)$$ None 0 2
9464.2.bp $$\chi_{9464}(5407, \cdot)$$ None 0 2
9464.2.by $$\chi_{9464}(1689, \cdot)$$ n/a 616 2
9464.2.bz $$\chi_{9464}(5071, \cdot)$$ None 0 2
9464.2.ca $$\chi_{9464}(1543, \cdot)$$ None 0 2
9464.2.cb $$\chi_{9464}(7121, \cdot)$$ n/a 616 2
9464.2.cc $$\chi_{9464}(3527, \cdot)$$ None 0 2
9464.2.ch $$\chi_{9464}(1205, \cdot)$$ n/a 1848 2
9464.2.ci $$\chi_{9464}(699, \cdot)$$ n/a 2424 2
9464.2.cj $$\chi_{9464}(6421, \cdot)$$ n/a 2424 2
9464.2.ck $$\chi_{9464}(339, \cdot)$$ n/a 2436 2
9464.2.cl $$\chi_{9464}(6275, \cdot)$$ n/a 2424 2
9464.2.cm $$\chi_{9464}(2389, \cdot)$$ n/a 2424 2
9464.2.cv $$\chi_{9464}(4203, \cdot)$$ n/a 2424 2
9464.2.cw $$\chi_{9464}(653, \cdot)$$ n/a 2424 2
9464.2.cx $$\chi_{9464}(6085, \cdot)$$ n/a 2436 2
9464.2.cy $$\chi_{9464}(675, \cdot)$$ n/a 2424 2
9464.2.cz $$\chi_{9464}(1037, \cdot)$$ n/a 1848 2
9464.2.da $$\chi_{9464}(867, \cdot)$$ n/a 2424 2
9464.2.df $$\chi_{9464}(1375, \cdot)$$ None 0 2
9464.2.dg $$\chi_{9464}(361, \cdot)$$ n/a 616 2
9464.2.dh $$\chi_{9464}(4247, \cdot)$$ None 0 2
9464.2.dl $$\chi_{9464}(2385, \cdot)$$ n/a 1232 4
9464.2.dm $$\chi_{9464}(695, \cdot)$$ None 0 4
9464.2.dp $$\chi_{9464}(3131, \cdot)$$ n/a 4848 4
9464.2.ds $$\chi_{9464}(5389, \cdot)$$ n/a 4848 4
9464.2.dt $$\chi_{9464}(437, \cdot)$$ n/a 4848 4
9464.2.du $$\chi_{9464}(995, \cdot)$$ n/a 3696 4
9464.2.dv $$\chi_{9464}(1451, \cdot)$$ n/a 4848 4
9464.2.dy $$\chi_{9464}(1333, \cdot)$$ n/a 4848 4
9464.2.eb $$\chi_{9464}(319, \cdot)$$ None 0 4
9464.2.ee $$\chi_{9464}(657, \cdot)$$ n/a 1232 4
9464.2.ef $$\chi_{9464}(577, \cdot)$$ n/a 1232 4
9464.2.eg $$\chi_{9464}(5727, \cdot)$$ None 0 4
9464.2.eh $$\chi_{9464}(1591, \cdot)$$ None 0 4
9464.2.ek $$\chi_{9464}(89, \cdot)$$ n/a 1232 4
9464.2.en $$\chi_{9464}(2117, \cdot)$$ n/a 4848 4
9464.2.eo $$\chi_{9464}(2347, \cdot)$$ n/a 4848 4
9464.2.eq $$\chi_{9464}(729, \cdot)$$ n/a 3288 12
9464.2.er $$\chi_{9464}(727, \cdot)$$ None 0 12
9464.2.ew $$\chi_{9464}(1065, \cdot)$$ n/a 3264 12
9464.2.ex $$\chi_{9464}(391, \cdot)$$ None 0 12
9464.2.ey $$\chi_{9464}(701, \cdot)$$ n/a 13104 12
9464.2.ez $$\chi_{9464}(27, \cdot)$$ n/a 17424 12
9464.2.fe $$\chi_{9464}(365, \cdot)$$ n/a 13104 12
9464.2.ff $$\chi_{9464}(363, \cdot)$$ n/a 17424 12
9464.2.fg $$\chi_{9464}(9, \cdot)$$ n/a 8736 24
9464.2.fh $$\chi_{9464}(113, \cdot)$$ n/a 6576 24
9464.2.fi $$\chi_{9464}(417, \cdot)$$ n/a 8736 24
9464.2.fj $$\chi_{9464}(289, \cdot)$$ n/a 8736 24
9464.2.fk $$\chi_{9464}(125, \cdot)$$ n/a 34848 24
9464.2.fn $$\chi_{9464}(603, \cdot)$$ n/a 26208 24
9464.2.fo $$\chi_{9464}(265, \cdot)$$ n/a 8736 24
9464.2.fr $$\chi_{9464}(463, \cdot)$$ None 0 24
9464.2.fu $$\chi_{9464}(367, \cdot)$$ None 0 24
9464.2.fv $$\chi_{9464}(121, \cdot)$$ n/a 8736 24
9464.2.fw $$\chi_{9464}(647, \cdot)$$ None 0 24
9464.2.gb $$\chi_{9464}(139, \cdot)$$ n/a 34848 24
9464.2.gc $$\chi_{9464}(309, \cdot)$$ n/a 26208 24
9464.2.gd $$\chi_{9464}(467, \cdot)$$ n/a 34848 24
9464.2.ge $$\chi_{9464}(53, \cdot)$$ n/a 34848 24
9464.2.gf $$\chi_{9464}(165, \cdot)$$ n/a 34848 24
9464.2.gg $$\chi_{9464}(75, \cdot)$$ n/a 34848 24
9464.2.gp $$\chi_{9464}(205, \cdot)$$ n/a 34848 24
9464.2.gq $$\chi_{9464}(451, \cdot)$$ n/a 34848 24
9464.2.gr $$\chi_{9464}(131, \cdot)$$ n/a 34848 24
9464.2.gs $$\chi_{9464}(389, \cdot)$$ n/a 34848 24
9464.2.gt $$\chi_{9464}(251, \cdot)$$ n/a 34848 24
9464.2.gu $$\chi_{9464}(29, \cdot)$$ n/a 26208 24
9464.2.gz $$\chi_{9464}(335, \cdot)$$ None 0 24
9464.2.ha $$\chi_{9464}(569, \cdot)$$ n/a 8736 24
9464.2.hb $$\chi_{9464}(87, \cdot)$$ None 0 24
9464.2.hc $$\chi_{9464}(495, \cdot)$$ None 0 24
9464.2.hd $$\chi_{9464}(25, \cdot)$$ n/a 8736 24
9464.2.hm $$\chi_{9464}(103, \cdot)$$ None 0 24
9464.2.hn $$\chi_{9464}(199, \cdot)$$ None 0 24
9464.2.ho $$\chi_{9464}(55, \cdot)$$ None 0 24
9464.2.hp $$\chi_{9464}(225, \cdot)$$ n/a 6528 24
9464.2.hu $$\chi_{9464}(283, \cdot)$$ n/a 34848 24
9464.2.hv $$\chi_{9464}(373, \cdot)$$ n/a 34848 24
9464.2.hw $$\chi_{9464}(3, \cdot)$$ n/a 34848 24
9464.2.hx $$\chi_{9464}(725, \cdot)$$ n/a 34848 24
9464.2.ia $$\chi_{9464}(11, \cdot)$$ n/a 69696 48
9464.2.id $$\chi_{9464}(397, \cdot)$$ n/a 69696 48
9464.2.ie $$\chi_{9464}(145, \cdot)$$ n/a 17472 48
9464.2.ig $$\chi_{9464}(135, \cdot)$$ None 0 48
9464.2.ih $$\chi_{9464}(15, \cdot)$$ None 0 48
9464.2.im $$\chi_{9464}(73, \cdot)$$ n/a 17472 48
9464.2.in $$\chi_{9464}(41, \cdot)$$ n/a 17472 48
9464.2.ip $$\chi_{9464}(487, \cdot)$$ None 0 48
9464.2.iq $$\chi_{9464}(45, \cdot)$$ n/a 69696 48
9464.2.is $$\chi_{9464}(291, \cdot)$$ n/a 69696 48
9464.2.it $$\chi_{9464}(267, \cdot)$$ n/a 52416 48
9464.2.iy $$\chi_{9464}(5, \cdot)$$ n/a 69696 48
9464.2.iz $$\chi_{9464}(293, \cdot)$$ n/a 69696 48
9464.2.jb $$\chi_{9464}(123, \cdot)$$ n/a 69696 48
9464.2.jc $$\chi_{9464}(375, \cdot)$$ None 0 48
9464.2.jf $$\chi_{9464}(33, \cdot)$$ n/a 17472 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(9464))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(9464)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(182))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(338))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(364))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(676))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(728))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1183))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1352))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2366))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4732))$$$$^{\oplus 2}$$