# Properties

 Label 5225.2 Level 5225 Weight 2 Dimension 967096 Nonzero newspaces 126 Sturm bound 4320000

## Defining parameters

 Level: $$N$$ = $$5225 = 5^{2} \cdot 11 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$126$$ Sturm bound: $$4320000$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5225))$$.

Total New Old
Modular forms 1090080 979644 110436
Cusp forms 1069921 967096 102825
Eisenstein series 20159 12548 7611

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5225))$$

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
5225.2.a $$\chi_{5225}(1, \cdot)$$ 5225.2.a.a 1 1
5225.2.a.b 1
5225.2.a.c 1
5225.2.a.d 2
5225.2.a.e 2
5225.2.a.f 2
5225.2.a.g 2
5225.2.a.h 5
5225.2.a.i 5
5225.2.a.j 5
5225.2.a.k 6
5225.2.a.l 6
5225.2.a.m 7
5225.2.a.n 7
5225.2.a.o 8
5225.2.a.p 9
5225.2.a.q 9
5225.2.a.r 15
5225.2.a.s 15
5225.2.a.t 15
5225.2.a.u 15
5225.2.a.v 15
5225.2.a.w 15
5225.2.a.x 15
5225.2.a.y 15
5225.2.a.z 16
5225.2.a.ba 20
5225.2.a.bb 22
5225.2.a.bc 30
5225.2.b $$\chi_{5225}(4599, \cdot)$$ n/a 268 1
5225.2.e $$\chi_{5225}(5224, \cdot)$$ n/a 356 1
5225.2.f $$\chi_{5225}(626, \cdot)$$ n/a 374 1
5225.2.i $$\chi_{5225}(1926, \cdot)$$ n/a 636 2
5225.2.j $$\chi_{5225}(1407, \cdot)$$ n/a 648 2
5225.2.m $$\chi_{5225}(2982, \cdot)$$ n/a 600 2
5225.2.n $$\chi_{5225}(3041, \cdot)$$ n/a 2160 4
5225.2.o $$\chi_{5225}(476, \cdot)$$ n/a 1368 4
5225.2.p $$\chi_{5225}(1046, \cdot)$$ n/a 1792 4
5225.2.q $$\chi_{5225}(1521, \cdot)$$ n/a 2160 4
5225.2.r $$\chi_{5225}(191, \cdot)$$ n/a 2160 4
5225.2.s $$\chi_{5225}(856, \cdot)$$ n/a 2160 4
5225.2.u $$\chi_{5225}(901, \cdot)$$ n/a 748 2
5225.2.x $$\chi_{5225}(274, \cdot)$$ n/a 712 2
5225.2.y $$\chi_{5225}(1299, \cdot)$$ n/a 600 2
5225.2.ba $$\chi_{5225}(826, \cdot)$$ n/a 1896 6
5225.2.bb $$\chi_{5225}(2659, \cdot)$$ n/a 2384 4
5225.2.be $$\chi_{5225}(2319, \cdot)$$ n/a 2160 4
5225.2.bg $$\chi_{5225}(3286, \cdot)$$ n/a 2384 4
5225.2.bm $$\chi_{5225}(816, \cdot)$$ n/a 2384 4
5225.2.bn $$\chi_{5225}(1671, \cdot)$$ n/a 2384 4
5225.2.bq $$\chi_{5225}(151, \cdot)$$ n/a 1496 4
5225.2.br $$\chi_{5225}(1766, \cdot)$$ n/a 2384 4
5225.2.bv $$\chi_{5225}(229, \cdot)$$ n/a 2160 4
5225.2.bw $$\chi_{5225}(1139, \cdot)$$ n/a 2384 4
5225.2.bz $$\chi_{5225}(189, \cdot)$$ n/a 2384 4
5225.2.ca $$\chi_{5225}(1899, \cdot)$$ n/a 1424 4
5225.2.cd $$\chi_{5225}(1044, \cdot)$$ n/a 2384 4
5225.2.ce $$\chi_{5225}(419, \cdot)$$ n/a 1808 4
5225.2.ch $$\chi_{5225}(324, \cdot)$$ n/a 1296 4
5225.2.ci $$\chi_{5225}(894, \cdot)$$ n/a 2160 4
5225.2.cl $$\chi_{5225}(2414, \cdot)$$ n/a 2160 4
5225.2.cm $$\chi_{5225}(94, \cdot)$$ n/a 2384 4
5225.2.cq $$\chi_{5225}(436, \cdot)$$ n/a 2384 4
5225.2.cr $$\chi_{5225}(1057, \cdot)$$ n/a 1200 4
5225.2.cu $$\chi_{5225}(1132, \cdot)$$ n/a 1424 4
5225.2.cv $$\chi_{5225}(581, \cdot)$$ n/a 4768 8
5225.2.cw $$\chi_{5225}(311, \cdot)$$ n/a 4768 8
5225.2.cx $$\chi_{5225}(691, \cdot)$$ n/a 4768 8
5225.2.cy $$\chi_{5225}(1071, \cdot)$$ n/a 4768 8
5225.2.cz $$\chi_{5225}(26, \cdot)$$ n/a 2992 8
5225.2.da $$\chi_{5225}(771, \cdot)$$ n/a 4000 8
5225.2.dc $$\chi_{5225}(1649, \cdot)$$ n/a 2136 6
5225.2.df $$\chi_{5225}(2276, \cdot)$$ n/a 2244 6
5225.2.dh $$\chi_{5225}(199, \cdot)$$ n/a 1800 6
5225.2.di $$\chi_{5225}(113, \cdot)$$ n/a 4768 8
5225.2.dl $$\chi_{5225}(2433, \cdot)$$ n/a 4320 8
5225.2.dm $$\chi_{5225}(248, \cdot)$$ n/a 4320 8
5225.2.do $$\chi_{5225}(37, \cdot)$$ n/a 4768 8
5225.2.dq $$\chi_{5225}(493, \cdot)$$ n/a 2848 8
5225.2.dr $$\chi_{5225}(683, \cdot)$$ n/a 4000 8
5225.2.ds $$\chi_{5225}(588, \cdot)$$ n/a 4768 8
5225.2.dx $$\chi_{5225}(723, \cdot)$$ n/a 4320 8
5225.2.eb $$\chi_{5225}(343, \cdot)$$ n/a 2592 8
5225.2.ec $$\chi_{5225}(172, \cdot)$$ n/a 4320 8
5225.2.ed $$\chi_{5225}(153, \cdot)$$ n/a 4320 8
5225.2.ef $$\chi_{5225}(322, \cdot)$$ n/a 4768 8
5225.2.eh $$\chi_{5225}(316, \cdot)$$ n/a 4768 8
5225.2.ej $$\chi_{5225}(84, \cdot)$$ n/a 4768 8
5225.2.em $$\chi_{5225}(444, \cdot)$$ n/a 4768 8
5225.2.en $$\chi_{5225}(144, \cdot)$$ n/a 4000 8
5225.2.eq $$\chi_{5225}(49, \cdot)$$ n/a 2848 8
5225.2.er $$\chi_{5225}(64, \cdot)$$ n/a 4768 8
5225.2.eu $$\chi_{5225}(259, \cdot)$$ n/a 4768 8
5225.2.ev $$\chi_{5225}(1399, \cdot)$$ n/a 2848 8
5225.2.ey $$\chi_{5225}(164, \cdot)$$ n/a 4768 8
5225.2.ez $$\chi_{5225}(1019, \cdot)$$ n/a 4768 8
5225.2.fc $$\chi_{5225}(334, \cdot)$$ n/a 4768 8
5225.2.fe $$\chi_{5225}(791, \cdot)$$ n/a 4768 8
5225.2.fh $$\chi_{5225}(426, \cdot)$$ n/a 2992 8
5225.2.fi $$\chi_{5225}(1646, \cdot)$$ n/a 4768 8
5225.2.fl $$\chi_{5225}(886, \cdot)$$ n/a 4768 8
5225.2.fr $$\chi_{5225}(46, \cdot)$$ n/a 4768 8
5225.2.ft $$\chi_{5225}(1204, \cdot)$$ n/a 4768 8
5225.2.fu $$\chi_{5225}(734, \cdot)$$ n/a 4768 8
5225.2.fx $$\chi_{5225}(43, \cdot)$$ n/a 4272 12
5225.2.fy $$\chi_{5225}(243, \cdot)$$ n/a 3600 12
5225.2.ga $$\chi_{5225}(111, \cdot)$$ n/a 12000 24
5225.2.gb $$\chi_{5225}(346, \cdot)$$ n/a 14304 24
5225.2.gc $$\chi_{5225}(251, \cdot)$$ n/a 8976 24
5225.2.gd $$\chi_{5225}(36, \cdot)$$ n/a 14304 24
5225.2.ge $$\chi_{5225}(16, \cdot)$$ n/a 14304 24
5225.2.gf $$\chi_{5225}(81, \cdot)$$ n/a 14304 24
5225.2.gg $$\chi_{5225}(27, \cdot)$$ n/a 9536 16
5225.2.gi $$\chi_{5225}(87, \cdot)$$ n/a 9536 16
5225.2.gj $$\chi_{5225}(277, \cdot)$$ n/a 9536 16
5225.2.gk $$\chi_{5225}(7, \cdot)$$ n/a 5696 16
5225.2.go $$\chi_{5225}(83, \cdot)$$ n/a 9536 16
5225.2.gt $$\chi_{5225}(103, \cdot)$$ n/a 9536 16
5225.2.gu $$\chi_{5225}(12, \cdot)$$ n/a 8000 16
5225.2.gv $$\chi_{5225}(768, \cdot)$$ n/a 5696 16
5225.2.gx $$\chi_{5225}(312, \cdot)$$ n/a 9536 16
5225.2.gz $$\chi_{5225}(387, \cdot)$$ n/a 9536 16
5225.2.ha $$\chi_{5225}(1052, \cdot)$$ n/a 9536 16
5225.2.hd $$\chi_{5225}(202, \cdot)$$ n/a 9536 16
5225.2.hf $$\chi_{5225}(109, \cdot)$$ n/a 14304 24
5225.2.hh $$\chi_{5225}(41, \cdot)$$ n/a 14304 24
5225.2.hk $$\chi_{5225}(4, \cdot)$$ n/a 14304 24
5225.2.hl $$\chi_{5225}(9, \cdot)$$ n/a 14304 24
5225.2.hm $$\chi_{5225}(289, \cdot)$$ n/a 14304 24
5225.2.hq $$\chi_{5225}(499, \cdot)$$ n/a 8544 24
5225.2.hs $$\chi_{5225}(336, \cdot)$$ n/a 14304 24
5225.2.ht $$\chi_{5225}(116, \cdot)$$ n/a 14304 24
5225.2.hu $$\chi_{5225}(261, \cdot)$$ n/a 14304 24
5225.2.hy $$\chi_{5225}(51, \cdot)$$ n/a 8976 24
5225.2.hz $$\chi_{5225}(104, \cdot)$$ n/a 14304 24
5225.2.ic $$\chi_{5225}(249, \cdot)$$ n/a 8544 24
5225.2.ig $$\chi_{5225}(79, \cdot)$$ n/a 14304 24
5225.2.ih $$\chi_{5225}(129, \cdot)$$ n/a 14304 24
5225.2.ii $$\chi_{5225}(29, \cdot)$$ n/a 14304 24
5225.2.ip $$\chi_{5225}(184, \cdot)$$ n/a 14304 24
5225.2.iq $$\chi_{5225}(309, \cdot)$$ n/a 12000 24
5225.2.is $$\chi_{5225}(21, \cdot)$$ n/a 14304 24
5225.2.iv $$\chi_{5225}(67, \cdot)$$ n/a 24000 48
5225.2.iw $$\chi_{5225}(142, \cdot)$$ n/a 28608 48
5225.2.iy $$\chi_{5225}(123, \cdot)$$ n/a 28608 48
5225.2.ja $$\chi_{5225}(53, \cdot)$$ n/a 28608 48
5225.2.je $$\chi_{5225}(257, \cdot)$$ n/a 17088 48
5225.2.jf $$\chi_{5225}(48, \cdot)$$ n/a 28608 48
5225.2.jg $$\chi_{5225}(3, \cdot)$$ n/a 28608 48
5225.2.jj $$\chi_{5225}(28, \cdot)$$ n/a 28608 48
5225.2.jk $$\chi_{5225}(118, \cdot)$$ n/a 17088 48
5225.2.jl $$\chi_{5225}(112, \cdot)$$ n/a 28608 48
5225.2.jp $$\chi_{5225}(17, \cdot)$$ n/a 28608 48
5225.2.jr $$\chi_{5225}(147, \cdot)$$ n/a 28608 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5225))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5225)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(209))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(275))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(475))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1045))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5225))$$$$^{\oplus 1}$$