Properties

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

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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

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