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Properties

Label 4256.2
Level 4256
Weight 2
Dimension 294724
Nonzero newspaces 96
Sturm bound 2211840

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Defining parameters

Level: \( N \) = \( 4256 = 2^{5} \cdot 7 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 96 \)
Sturm bound: \(2211840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4256))\).

Total New Old
Modular forms 559872 298124 261748
Cusp forms 546049 294724 251325
Eisenstein series 13823 3400 10423

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4256))\)

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
4256.2.a \(\chi_{4256}(1, \cdot)\) 4256.2.a.a 1 1
4256.2.a.b 1
4256.2.a.c 2
4256.2.a.d 2
4256.2.a.e 4
4256.2.a.f 4
4256.2.a.g 5
4256.2.a.h 5
4256.2.a.i 6
4256.2.a.j 6
4256.2.a.k 6
4256.2.a.l 6
4256.2.a.m 6
4256.2.a.n 6
4256.2.a.o 7
4256.2.a.p 7
4256.2.a.q 7
4256.2.a.r 7
4256.2.a.s 10
4256.2.a.t 10
4256.2.b \(\chi_{4256}(2129, \cdot)\) n/a 108 1
4256.2.e \(\chi_{4256}(911, \cdot)\) n/a 120 1
4256.2.f \(\chi_{4256}(1329, \cdot)\) n/a 156 1
4256.2.i \(\chi_{4256}(4143, \cdot)\) n/a 144 1
4256.2.j \(\chi_{4256}(2015, \cdot)\) n/a 144 1
4256.2.m \(\chi_{4256}(3457, \cdot)\) n/a 160 1
4256.2.n \(\chi_{4256}(3039, \cdot)\) n/a 120 1
4256.2.q \(\chi_{4256}(2433, \cdot)\) n/a 288 2
4256.2.r \(\chi_{4256}(1569, \cdot)\) n/a 240 2
4256.2.s \(\chi_{4256}(1185, \cdot)\) n/a 320 2
4256.2.t \(\chi_{4256}(961, \cdot)\) n/a 320 2
4256.2.u \(\chi_{4256}(265, \cdot)\) None 0 2
4256.2.v \(\chi_{4256}(951, \cdot)\) None 0 2
4256.2.ba \(\chi_{4256}(1065, \cdot)\) None 0 2
4256.2.bb \(\chi_{4256}(1975, \cdot)\) None 0 2
4256.2.bc \(\chi_{4256}(2063, \cdot)\) n/a 312 2
4256.2.bf \(\chi_{4256}(369, \cdot)\) n/a 312 2
4256.2.bg \(\chi_{4256}(1551, \cdot)\) n/a 312 2
4256.2.bj \(\chi_{4256}(2097, \cdot)\) n/a 312 2
4256.2.bk \(\chi_{4256}(2273, \cdot)\) n/a 320 2
4256.2.bn \(\chi_{4256}(159, \cdot)\) n/a 320 2
4256.2.bp \(\chi_{4256}(1247, \cdot)\) n/a 240 2
4256.2.br \(\chi_{4256}(1215, \cdot)\) n/a 320 2
4256.2.bv \(\chi_{4256}(3583, \cdot)\) n/a 320 2
4256.2.bx \(\chi_{4256}(1025, \cdot)\) n/a 320 2
4256.2.by \(\chi_{4256}(2623, \cdot)\) n/a 288 2
4256.2.ca \(\chi_{4256}(1665, \cdot)\) n/a 320 2
4256.2.ce \(\chi_{4256}(639, \cdot)\) n/a 320 2
4256.2.cf \(\chi_{4256}(1775, \cdot)\) n/a 312 2
4256.2.ci \(\chi_{4256}(1873, \cdot)\) n/a 312 2
4256.2.ck \(\chi_{4256}(3793, \cdot)\) n/a 312 2
4256.2.cm \(\chi_{4256}(495, \cdot)\) n/a 288 2
4256.2.cn \(\chi_{4256}(1937, \cdot)\) n/a 312 2
4256.2.cp \(\chi_{4256}(1455, \cdot)\) n/a 312 2
4256.2.cs \(\chi_{4256}(3697, \cdot)\) n/a 240 2
4256.2.cu \(\chi_{4256}(303, \cdot)\) n/a 312 2
4256.2.cv \(\chi_{4256}(305, \cdot)\) n/a 288 2
4256.2.cx \(\chi_{4256}(3375, \cdot)\) n/a 240 2
4256.2.cz \(\chi_{4256}(2287, \cdot)\) n/a 312 2
4256.2.dc \(\chi_{4256}(145, \cdot)\) n/a 312 2
4256.2.df \(\chi_{4256}(863, \cdot)\) n/a 320 2
4256.2.dg \(\chi_{4256}(2497, \cdot)\) n/a 320 2
4256.2.dj \(\chi_{4256}(1375, \cdot)\) n/a 320 2
4256.2.dk \(\chi_{4256}(379, \cdot)\) n/a 1920 4
4256.2.dl \(\chi_{4256}(533, \cdot)\) n/a 1728 4
4256.2.dq \(\chi_{4256}(419, \cdot)\) n/a 2304 4
4256.2.dr \(\chi_{4256}(797, \cdot)\) n/a 2544 4
4256.2.ds \(\chi_{4256}(225, \cdot)\) n/a 720 6
4256.2.dt \(\chi_{4256}(289, \cdot)\) n/a 960 6
4256.2.du \(\chi_{4256}(1089, \cdot)\) n/a 960 6
4256.2.dx \(\chi_{4256}(1033, \cdot)\) None 0 4
4256.2.dy \(\chi_{4256}(487, \cdot)\) None 0 4
4256.2.dz \(\chi_{4256}(297, \cdot)\) None 0 4
4256.2.ea \(\chi_{4256}(311, \cdot)\) None 0 4
4256.2.ef \(\chi_{4256}(647, \cdot)\) None 0 4
4256.2.eg \(\chi_{4256}(873, \cdot)\) None 0 4
4256.2.eh \(\chi_{4256}(711, \cdot)\) None 0 4
4256.2.ei \(\chi_{4256}(183, \cdot)\) None 0 4
4256.2.ej \(\chi_{4256}(121, \cdot)\) None 0 4
4256.2.ek \(\chi_{4256}(505, \cdot)\) None 0 4
4256.2.et \(\chi_{4256}(87, \cdot)\) None 0 4
4256.2.eu \(\chi_{4256}(391, \cdot)\) None 0 4
4256.2.ev \(\chi_{4256}(521, \cdot)\) None 0 4
4256.2.ew \(\chi_{4256}(601, \cdot)\) None 0 4
4256.2.ex \(\chi_{4256}(151, \cdot)\) None 0 4
4256.2.ey \(\chi_{4256}(457, \cdot)\) None 0 4
4256.2.fb \(\chi_{4256}(479, \cdot)\) n/a 960 6
4256.2.fc \(\chi_{4256}(319, \cdot)\) n/a 960 6
4256.2.ff \(\chi_{4256}(241, \cdot)\) n/a 936 6
4256.2.fg \(\chi_{4256}(625, \cdot)\) n/a 936 6
4256.2.fl \(\chi_{4256}(97, \cdot)\) n/a 960 6
4256.2.fo \(\chi_{4256}(257, \cdot)\) n/a 960 6
4256.2.fr \(\chi_{4256}(111, \cdot)\) n/a 936 6
4256.2.fs \(\chi_{4256}(15, \cdot)\) n/a 720 6
4256.2.fv \(\chi_{4256}(751, \cdot)\) n/a 936 6
4256.2.fw \(\chi_{4256}(47, \cdot)\) n/a 936 6
4256.2.fz \(\chi_{4256}(127, \cdot)\) n/a 720 6
4256.2.ga \(\chi_{4256}(671, \cdot)\) n/a 960 6
4256.2.gd \(\chi_{4256}(1279, \cdot)\) n/a 960 6
4256.2.ge \(\chi_{4256}(991, \cdot)\) n/a 960 6
4256.2.gh \(\chi_{4256}(785, \cdot)\) n/a 720 6
4256.2.gi \(\chi_{4256}(433, \cdot)\) n/a 936 6
4256.2.gl \(\chi_{4256}(1041, \cdot)\) n/a 936 6
4256.2.gm \(\chi_{4256}(81, \cdot)\) n/a 936 6
4256.2.gn \(\chi_{4256}(33, \cdot)\) n/a 960 6
4256.2.gq \(\chi_{4256}(79, \cdot)\) n/a 936 6
4256.2.gr \(\chi_{4256}(271, \cdot)\) n/a 936 6
4256.2.gw \(\chi_{4256}(837, \cdot)\) n/a 4608 8
4256.2.gx \(\chi_{4256}(683, \cdot)\) n/a 5088 8
4256.2.ha \(\chi_{4256}(619, \cdot)\) n/a 5088 8
4256.2.hb \(\chi_{4256}(677, \cdot)\) n/a 5088 8
4256.2.hc \(\chi_{4256}(69, \cdot)\) n/a 5088 8
4256.2.hd \(\chi_{4256}(83, \cdot)\) n/a 5088 8
4256.2.hi \(\chi_{4256}(829, \cdot)\) n/a 5088 8
4256.2.hj \(\chi_{4256}(467, \cdot)\) n/a 5088 8
4256.2.hk \(\chi_{4256}(429, \cdot)\) n/a 5088 8
4256.2.hl \(\chi_{4256}(331, \cdot)\) n/a 5088 8
4256.2.hq \(\chi_{4256}(107, \cdot)\) n/a 5088 8
4256.2.hr \(\chi_{4256}(277, \cdot)\) n/a 5088 8
4256.2.hs \(\chi_{4256}(197, \cdot)\) n/a 3840 8
4256.2.ht \(\chi_{4256}(715, \cdot)\) n/a 3840 8
4256.2.hw \(\chi_{4256}(341, \cdot)\) n/a 5088 8
4256.2.hx \(\chi_{4256}(115, \cdot)\) n/a 4608 8
4256.2.ie \(\chi_{4256}(169, \cdot)\) None 0 12
4256.2.if \(\chi_{4256}(41, \cdot)\) None 0 12
4256.2.ig \(\chi_{4256}(199, \cdot)\) None 0 12
4256.2.ih \(\chi_{4256}(135, \cdot)\) None 0 12
4256.2.ii \(\chi_{4256}(25, \cdot)\) None 0 12
4256.2.ij \(\chi_{4256}(409, \cdot)\) None 0 12
4256.2.ik \(\chi_{4256}(55, \cdot)\) None 0 12
4256.2.il \(\chi_{4256}(71, \cdot)\) None 0 12
4256.2.iu \(\chi_{4256}(375, \cdot)\) None 0 12
4256.2.iv \(\chi_{4256}(215, \cdot)\) None 0 12
4256.2.iw \(\chi_{4256}(89, \cdot)\) None 0 12
4256.2.ix \(\chi_{4256}(9, \cdot)\) None 0 12
4256.2.jc \(\chi_{4256}(93, \cdot)\) n/a 15264 24
4256.2.jd \(\chi_{4256}(139, \cdot)\) n/a 15264 24
4256.2.je \(\chi_{4256}(85, \cdot)\) n/a 11520 24
4256.2.jf \(\chi_{4256}(131, \cdot)\) n/a 15264 24
4256.2.jg \(\chi_{4256}(117, \cdot)\) n/a 15264 24
4256.2.jh \(\chi_{4256}(155, \cdot)\) n/a 11520 24
4256.2.ji \(\chi_{4256}(13, \cdot)\) n/a 15264 24
4256.2.jj \(\chi_{4256}(67, \cdot)\) n/a 15264 24
4256.2.js \(\chi_{4256}(51, \cdot)\) n/a 15264 24
4256.2.jt \(\chi_{4256}(269, \cdot)\) n/a 15264 24
4256.2.ju \(\chi_{4256}(283, \cdot)\) n/a 15264 24
4256.2.jv \(\chi_{4256}(541, \cdot)\) n/a 15264 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4256))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4256)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(532))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(608))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1064))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4256))\)\(^{\oplus 1}\)