# Properties

 Label 4560.2 Level 4560 Weight 2 Dimension 211736 Nonzero newspaces 84 Sturm bound 2211840

## Defining parameters

 Level: $$N$$ = $$4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$84$$ Sturm bound: $$2211840$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4560))$$.

Total New Old
Modular forms 561024 213568 347456
Cusp forms 544897 211736 333161
Eisenstein series 16127 1832 14295

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4560))$$

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
4560.2.a $$\chi_{4560}(1, \cdot)$$ 4560.2.a.a 1 1
4560.2.a.b 1
4560.2.a.c 1
4560.2.a.d 1
4560.2.a.e 1
4560.2.a.f 1
4560.2.a.g 1
4560.2.a.h 1
4560.2.a.i 1
4560.2.a.j 1
4560.2.a.k 1
4560.2.a.l 1
4560.2.a.m 1
4560.2.a.n 1
4560.2.a.o 1
4560.2.a.p 1
4560.2.a.q 1
4560.2.a.r 1
4560.2.a.s 1
4560.2.a.t 1
4560.2.a.u 1
4560.2.a.v 1
4560.2.a.w 1
4560.2.a.x 1
4560.2.a.y 1
4560.2.a.z 1
4560.2.a.ba 1
4560.2.a.bb 1
4560.2.a.bc 1
4560.2.a.bd 1
4560.2.a.be 2
4560.2.a.bf 2
4560.2.a.bg 2
4560.2.a.bh 2
4560.2.a.bi 2
4560.2.a.bj 2
4560.2.a.bk 2
4560.2.a.bl 2
4560.2.a.bm 2
4560.2.a.bn 2
4560.2.a.bo 2
4560.2.a.bp 2
4560.2.a.bq 3
4560.2.a.br 3
4560.2.a.bs 3
4560.2.a.bt 3
4560.2.a.bu 3
4560.2.a.bv 3
4560.2.c $$\chi_{4560}(2471, \cdot)$$ None 0 1
4560.2.d $$\chi_{4560}(2431, \cdot)$$ 4560.2.d.a 2 1
4560.2.d.b 2
4560.2.d.c 2
4560.2.d.d 2
4560.2.d.e 6
4560.2.d.f 6
4560.2.d.g 6
4560.2.d.h 6
4560.2.d.i 12
4560.2.d.j 12
4560.2.d.k 12
4560.2.d.l 12
4560.2.f $$\chi_{4560}(1369, \cdot)$$ None 0 1
4560.2.i $$\chi_{4560}(2849, \cdot)$$ n/a 236 1
4560.2.j $$\chi_{4560}(3649, \cdot)$$ n/a 108 1
4560.2.m $$\chi_{4560}(569, \cdot)$$ None 0 1
4560.2.o $$\chi_{4560}(191, \cdot)$$ n/a 144 1
4560.2.p $$\chi_{4560}(151, \cdot)$$ None 0 1
4560.2.r $$\chi_{4560}(3761, \cdot)$$ n/a 160 1
4560.2.u $$\chi_{4560}(2281, \cdot)$$ None 0 1
4560.2.w $$\chi_{4560}(1519, \cdot)$$ n/a 120 1
4560.2.x $$\chi_{4560}(1559, \cdot)$$ None 0 1
4560.2.ba $$\chi_{4560}(3799, \cdot)$$ None 0 1
4560.2.bb $$\chi_{4560}(3839, \cdot)$$ n/a 216 1
4560.2.bd $$\chi_{4560}(1481, \cdot)$$ None 0 1
4560.2.bg $$\chi_{4560}(961, \cdot)$$ n/a 160 2
4560.2.bi $$\chi_{4560}(379, \cdot)$$ n/a 960 2
4560.2.bj $$\chi_{4560}(341, \cdot)$$ n/a 1280 2
4560.2.bm $$\chi_{4560}(1141, \cdot)$$ n/a 576 2
4560.2.bn $$\chi_{4560}(419, \cdot)$$ n/a 1728 2
4560.2.bp $$\chi_{4560}(1177, \cdot)$$ None 0 2
4560.2.bs $$\chi_{4560}(2623, \cdot)$$ n/a 216 2
4560.2.bu $$\chi_{4560}(1217, \cdot)$$ n/a 432 2
4560.2.bv $$\chi_{4560}(1367, \cdot)$$ None 0 2
4560.2.by $$\chi_{4560}(3307, \cdot)$$ n/a 864 2
4560.2.ca $$\chi_{4560}(2317, \cdot)$$ n/a 960 2
4560.2.cb $$\chi_{4560}(227, \cdot)$$ n/a 1904 2
4560.2.cd $$\chi_{4560}(2357, \cdot)$$ n/a 1728 2
4560.2.cf $$\chi_{4560}(1027, \cdot)$$ n/a 864 2
4560.2.ch $$\chi_{4560}(37, \cdot)$$ n/a 960 2
4560.2.ck $$\chi_{4560}(2507, \cdot)$$ n/a 1904 2
4560.2.cm $$\chi_{4560}(77, \cdot)$$ n/a 1728 2
4560.2.cn $$\chi_{4560}(1673, \cdot)$$ None 0 2
4560.2.cq $$\chi_{4560}(1823, \cdot)$$ n/a 480 2
4560.2.cs $$\chi_{4560}(1633, \cdot)$$ n/a 240 2
4560.2.ct $$\chi_{4560}(343, \cdot)$$ None 0 2
4560.2.cv $$\chi_{4560}(1331, \cdot)$$ n/a 1152 2
4560.2.cy $$\chi_{4560}(229, \cdot)$$ n/a 864 2
4560.2.cz $$\chi_{4560}(1709, \cdot)$$ n/a 1904 2
4560.2.dc $$\chi_{4560}(1291, \cdot)$$ n/a 640 2
4560.2.dd $$\chi_{4560}(449, \cdot)$$ n/a 472 2
4560.2.dg $$\chi_{4560}(2329, \cdot)$$ None 0 2
4560.2.di $$\chi_{4560}(31, \cdot)$$ n/a 160 2
4560.2.dj $$\chi_{4560}(311, \cdot)$$ None 0 2
4560.2.dm $$\chi_{4560}(2311, \cdot)$$ None 0 2
4560.2.dn $$\chi_{4560}(1151, \cdot)$$ n/a 320 2
4560.2.dp $$\chi_{4560}(2729, \cdot)$$ None 0 2
4560.2.ds $$\chi_{4560}(49, \cdot)$$ n/a 240 2
4560.2.du $$\chi_{4560}(2519, \cdot)$$ None 0 2
4560.2.dv $$\chi_{4560}(559, \cdot)$$ n/a 240 2
4560.2.dx $$\chi_{4560}(121, \cdot)$$ None 0 2
4560.2.ea $$\chi_{4560}(1361, \cdot)$$ n/a 320 2
4560.2.ed $$\chi_{4560}(521, \cdot)$$ None 0 2
4560.2.ef $$\chi_{4560}(239, \cdot)$$ n/a 480 2
4560.2.eg $$\chi_{4560}(1399, \cdot)$$ None 0 2
4560.2.ei $$\chi_{4560}(481, \cdot)$$ n/a 480 6
4560.2.ej $$\chi_{4560}(539, \cdot)$$ n/a 3808 4
4560.2.em $$\chi_{4560}(1261, \cdot)$$ n/a 1280 4
4560.2.en $$\chi_{4560}(221, \cdot)$$ n/a 2560 4
4560.2.eq $$\chi_{4560}(259, \cdot)$$ n/a 1920 4
4560.2.es $$\chi_{4560}(407, \cdot)$$ None 0 4
4560.2.et $$\chi_{4560}(353, \cdot)$$ n/a 944 4
4560.2.ev $$\chi_{4560}(463, \cdot)$$ n/a 480 4
4560.2.ey $$\chi_{4560}(217, \cdot)$$ None 0 4
4560.2.fa $$\chi_{4560}(2197, \cdot)$$ n/a 1920 4
4560.2.fc $$\chi_{4560}(1987, \cdot)$$ n/a 1920 4
4560.2.fd $$\chi_{4560}(1037, \cdot)$$ n/a 3808 4
4560.2.ff $$\chi_{4560}(107, \cdot)$$ n/a 3808 4
4560.2.fh $$\chi_{4560}(373, \cdot)$$ n/a 1920 4
4560.2.fj $$\chi_{4560}(163, \cdot)$$ n/a 1920 4
4560.2.fm $$\chi_{4560}(197, \cdot)$$ n/a 3808 4
4560.2.fo $$\chi_{4560}(2387, \cdot)$$ n/a 3808 4
4560.2.fq $$\chi_{4560}(7, \cdot)$$ None 0 4
4560.2.fr $$\chi_{4560}(673, \cdot)$$ n/a 480 4
4560.2.ft $$\chi_{4560}(863, \cdot)$$ n/a 960 4
4560.2.fw $$\chi_{4560}(1337, \cdot)$$ None 0 4
4560.2.fy $$\chi_{4560}(331, \cdot)$$ n/a 1280 4
4560.2.fz $$\chi_{4560}(749, \cdot)$$ n/a 3808 4
4560.2.gc $$\chi_{4560}(349, \cdot)$$ n/a 1920 4
4560.2.gd $$\chi_{4560}(11, \cdot)$$ n/a 2560 4
4560.2.gg $$\chi_{4560}(439, \cdot)$$ None 0 6
4560.2.gj $$\chi_{4560}(479, \cdot)$$ n/a 1440 6
4560.2.gk $$\chi_{4560}(41, \cdot)$$ None 0 6
4560.2.gn $$\chi_{4560}(841, \cdot)$$ None 0 6
4560.2.go $$\chi_{4560}(79, \cdot)$$ n/a 720 6
4560.2.gr $$\chi_{4560}(401, \cdot)$$ n/a 960 6
4560.2.gs $$\chi_{4560}(119, \cdot)$$ None 0 6
4560.2.gv $$\chi_{4560}(289, \cdot)$$ n/a 720 6
4560.2.gw $$\chi_{4560}(1351, \cdot)$$ None 0 6
4560.2.gz $$\chi_{4560}(89, \cdot)$$ None 0 6
4560.2.ha $$\chi_{4560}(671, \cdot)$$ n/a 960 6
4560.2.hd $$\chi_{4560}(751, \cdot)$$ n/a 480 6
4560.2.he $$\chi_{4560}(169, \cdot)$$ None 0 6
4560.2.hh $$\chi_{4560}(1031, \cdot)$$ None 0 6
4560.2.hi $$\chi_{4560}(1169, \cdot)$$ n/a 1416 6
4560.2.hk $$\chi_{4560}(709, \cdot)$$ n/a 5760 12
4560.2.hm $$\chi_{4560}(91, \cdot)$$ n/a 3840 12
4560.2.ho $$\chi_{4560}(131, \cdot)$$ n/a 7680 12
4560.2.hq $$\chi_{4560}(29, \cdot)$$ n/a 11424 12
4560.2.ht $$\chi_{4560}(143, \cdot)$$ n/a 2880 12
4560.2.hu $$\chi_{4560}(137, \cdot)$$ None 0 12
4560.2.hx $$\chi_{4560}(97, \cdot)$$ n/a 1440 12
4560.2.hy $$\chi_{4560}(727, \cdot)$$ None 0 12
4560.2.ia $$\chi_{4560}(917, \cdot)$$ n/a 11424 12
4560.2.ic $$\chi_{4560}(203, \cdot)$$ n/a 11424 12
4560.2.if $$\chi_{4560}(827, \cdot)$$ n/a 11424 12
4560.2.ih $$\chi_{4560}(557, \cdot)$$ n/a 11424 12
4560.2.ii $$\chi_{4560}(637, \cdot)$$ n/a 5760 12
4560.2.ik $$\chi_{4560}(187, \cdot)$$ n/a 5760 12
4560.2.in $$\chi_{4560}(43, \cdot)$$ n/a 5760 12
4560.2.ip $$\chi_{4560}(13, \cdot)$$ n/a 5760 12
4560.2.iq $$\chi_{4560}(17, \cdot)$$ n/a 2832 12
4560.2.it $$\chi_{4560}(167, \cdot)$$ None 0 12
4560.2.iu $$\chi_{4560}(367, \cdot)$$ n/a 1440 12
4560.2.ix $$\chi_{4560}(553, \cdot)$$ None 0 12
4560.2.iz $$\chi_{4560}(979, \cdot)$$ n/a 5760 12
4560.2.jb $$\chi_{4560}(61, \cdot)$$ n/a 3840 12
4560.2.jd $$\chi_{4560}(941, \cdot)$$ n/a 7680 12
4560.2.jf $$\chi_{4560}(899, \cdot)$$ n/a 11424 12

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4560))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4560)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(228))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(240))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(285))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(380))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(456))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(570))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(760))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(912))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1140))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1520))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2280))$$$$^{\oplus 2}$$