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Properties

Label 5456.2
Level 5456
Weight 2
Dimension 506348
Nonzero newspaces 112
Sturm bound 3686400

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Defining parameters

Level: \( N \) = \( 5456 = 2^{4} \cdot 11 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 112 \)
Sturm bound: \(3686400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5456))\).

Total New Old
Modular forms 930000 511048 418952
Cusp forms 913201 506348 406853
Eisenstein series 16799 4700 12099

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5456))\)

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
5456.2.a \(\chi_{5456}(1, \cdot)\) 5456.2.a.a 1 1
5456.2.a.b 1
5456.2.a.c 1
5456.2.a.d 1
5456.2.a.e 1
5456.2.a.f 1
5456.2.a.g 1
5456.2.a.h 1
5456.2.a.i 1
5456.2.a.j 2
5456.2.a.k 2
5456.2.a.l 2
5456.2.a.m 2
5456.2.a.n 2
5456.2.a.o 2
5456.2.a.p 2
5456.2.a.q 2
5456.2.a.r 2
5456.2.a.s 3
5456.2.a.t 3
5456.2.a.u 4
5456.2.a.v 4
5456.2.a.w 4
5456.2.a.x 5
5456.2.a.y 6
5456.2.a.z 7
5456.2.a.ba 8
5456.2.a.bb 8
5456.2.a.bc 9
5456.2.a.bd 9
5456.2.a.be 10
5456.2.a.bf 10
5456.2.a.bg 10
5456.2.a.bh 11
5456.2.a.bi 12
5456.2.c \(\chi_{5456}(3719, \cdot)\) None 0 1
5456.2.d \(\chi_{5456}(2729, \cdot)\) None 0 1
5456.2.f \(\chi_{5456}(3409, \cdot)\) n/a 190 1
5456.2.i \(\chi_{5456}(1055, \cdot)\) n/a 180 1
5456.2.k \(\chi_{5456}(681, \cdot)\) None 0 1
5456.2.l \(\chi_{5456}(3783, \cdot)\) None 0 1
5456.2.n \(\chi_{5456}(991, \cdot)\) n/a 160 1
5456.2.q \(\chi_{5456}(1761, \cdot)\) n/a 320 2
5456.2.s \(\chi_{5456}(2419, \cdot)\) n/a 1440 2
5456.2.t \(\chi_{5456}(1365, \cdot)\) n/a 1200 2
5456.2.w \(\chi_{5456}(2045, \cdot)\) n/a 1528 2
5456.2.x \(\chi_{5456}(2355, \cdot)\) n/a 1280 2
5456.2.z \(\chi_{5456}(993, \cdot)\) n/a 720 4
5456.2.ba \(\chi_{5456}(3073, \cdot)\) n/a 760 4
5456.2.bb \(\chi_{5456}(2017, \cdot)\) n/a 760 4
5456.2.bc \(\chi_{5456}(97, \cdot)\) n/a 760 4
5456.2.bd \(\chi_{5456}(529, \cdot)\) n/a 640 4
5456.2.be \(\chi_{5456}(977, \cdot)\) n/a 760 4
5456.2.bh \(\chi_{5456}(4335, \cdot)\) n/a 320 2
5456.2.bj \(\chi_{5456}(87, \cdot)\) None 0 2
5456.2.bk \(\chi_{5456}(4025, \cdot)\) None 0 2
5456.2.bm \(\chi_{5456}(2815, \cdot)\) n/a 384 2
5456.2.bp \(\chi_{5456}(1297, \cdot)\) n/a 380 2
5456.2.br \(\chi_{5456}(4489, \cdot)\) None 0 2
5456.2.bs \(\chi_{5456}(1607, \cdot)\) None 0 2
5456.2.bu \(\chi_{5456}(1647, \cdot)\) n/a 768 4
5456.2.bx \(\chi_{5456}(833, \cdot)\) n/a 760 4
5456.2.bz \(\chi_{5456}(2457, \cdot)\) None 0 4
5456.2.ca \(\chi_{5456}(1511, \cdot)\) None 0 4
5456.2.cc \(\chi_{5456}(791, \cdot)\) None 0 4
5456.2.cf \(\chi_{5456}(153, \cdot)\) None 0 4
5456.2.ch \(\chi_{5456}(15, \cdot)\) n/a 768 4
5456.2.cm \(\chi_{5456}(1263, \cdot)\) n/a 768 4
5456.2.co \(\chi_{5456}(1983, \cdot)\) n/a 768 4
5456.2.cq \(\chi_{5456}(511, \cdot)\) n/a 768 4
5456.2.cs \(\chi_{5456}(457, \cdot)\) None 0 4
5456.2.cv \(\chi_{5456}(343, \cdot)\) None 0 4
5456.2.cx \(\chi_{5456}(1799, \cdot)\) None 0 4
5456.2.cz \(\chi_{5456}(2823, \cdot)\) None 0 4
5456.2.da \(\chi_{5456}(2569, \cdot)\) None 0 4
5456.2.dc \(\chi_{5456}(1449, \cdot)\) None 0 4
5456.2.de \(\chi_{5456}(2169, \cdot)\) None 0 4
5456.2.dh \(\chi_{5456}(39, \cdot)\) None 0 4
5456.2.dj \(\chi_{5456}(463, \cdot)\) n/a 640 4
5456.2.dl \(\chi_{5456}(969, \cdot)\) None 0 4
5456.2.do \(\chi_{5456}(23, \cdot)\) None 0 4
5456.2.dq \(\chi_{5456}(1889, \cdot)\) n/a 760 4
5456.2.dr \(\chi_{5456}(95, \cdot)\) n/a 768 4
5456.2.dt \(\chi_{5456}(1151, \cdot)\) n/a 768 4
5456.2.dv \(\chi_{5456}(63, \cdot)\) n/a 720 4
5456.2.dy \(\chi_{5456}(337, \cdot)\) n/a 760 4
5456.2.ea \(\chi_{5456}(1425, \cdot)\) n/a 760 4
5456.2.ec \(\chi_{5456}(1201, \cdot)\) n/a 760 4
5456.2.ed \(\chi_{5456}(591, \cdot)\) n/a 768 4
5456.2.ef \(\chi_{5456}(647, \cdot)\) None 0 4
5456.2.ei \(\chi_{5456}(729, \cdot)\) None 0 4
5456.2.ek \(\chi_{5456}(1241, \cdot)\) None 0 4
5456.2.em \(\chi_{5456}(345, \cdot)\) None 0 4
5456.2.en \(\chi_{5456}(247, \cdot)\) None 0 4
5456.2.ep \(\chi_{5456}(1015, \cdot)\) None 0 4
5456.2.er \(\chi_{5456}(2247, \cdot)\) None 0 4
5456.2.eu \(\chi_{5456}(1225, \cdot)\) None 0 4
5456.2.ew \(\chi_{5456}(1583, \cdot)\) n/a 768 4
5456.2.ex \(\chi_{5456}(945, \cdot)\) n/a 760 4
5456.2.fb \(\chi_{5456}(399, \cdot)\) n/a 768 4
5456.2.fd \(\chi_{5456}(535, \cdot)\) None 0 4
5456.2.fe \(\chi_{5456}(953, \cdot)\) None 0 4
5456.2.fg \(\chi_{5456}(285, \cdot)\) n/a 3056 4
5456.2.fj \(\chi_{5456}(243, \cdot)\) n/a 2560 4
5456.2.fk \(\chi_{5456}(1451, \cdot)\) n/a 3056 4
5456.2.fn \(\chi_{5456}(397, \cdot)\) n/a 2560 4
5456.2.fo \(\chi_{5456}(113, \cdot)\) n/a 1520 8
5456.2.fp \(\chi_{5456}(1409, \cdot)\) n/a 1280 8
5456.2.fq \(\chi_{5456}(289, \cdot)\) n/a 1520 8
5456.2.fr \(\chi_{5456}(81, \cdot)\) n/a 1520 8
5456.2.fs \(\chi_{5456}(273, \cdot)\) n/a 1520 8
5456.2.ft \(\chi_{5456}(49, \cdot)\) n/a 1520 8
5456.2.fv \(\chi_{5456}(157, \cdot)\) n/a 6112 8
5456.2.fw \(\chi_{5456}(35, \cdot)\) n/a 6112 8
5456.2.fz \(\chi_{5456}(147, \cdot)\) n/a 6112 8
5456.2.ga \(\chi_{5456}(1069, \cdot)\) n/a 6112 8
5456.2.gd \(\chi_{5456}(85, \cdot)\) n/a 6112 8
5456.2.gf \(\chi_{5456}(619, \cdot)\) n/a 6112 8
5456.2.gh \(\chi_{5456}(771, \cdot)\) n/a 5120 8
5456.2.gj \(\chi_{5456}(27, \cdot)\) n/a 6112 8
5456.2.gk \(\chi_{5456}(461, \cdot)\) n/a 6112 8
5456.2.gm \(\chi_{5456}(29, \cdot)\) n/a 6112 8
5456.2.go \(\chi_{5456}(61, \cdot)\) n/a 6112 8
5456.2.gq \(\chi_{5456}(339, \cdot)\) n/a 6112 8
5456.2.gt \(\chi_{5456}(1093, \cdot)\) n/a 6112 8
5456.2.gu \(\chi_{5456}(283, \cdot)\) n/a 6112 8
5456.2.gx \(\chi_{5456}(171, \cdot)\) n/a 6112 8
5456.2.gz \(\chi_{5456}(125, \cdot)\) n/a 5760 8
5456.2.hb \(\chi_{5456}(221, \cdot)\) n/a 5120 8
5456.2.hd \(\chi_{5456}(653, \cdot)\) n/a 6112 8
5456.2.he \(\chi_{5456}(219, \cdot)\) n/a 6112 8
5456.2.hg \(\chi_{5456}(1163, \cdot)\) n/a 6112 8
5456.2.hi \(\chi_{5456}(435, \cdot)\) n/a 5760 8
5456.2.hk \(\chi_{5456}(357, \cdot)\) n/a 6112 8
5456.2.hn \(\chi_{5456}(91, \cdot)\) n/a 6112 8
5456.2.ho \(\chi_{5456}(525, \cdot)\) n/a 6112 8
5456.2.hr \(\chi_{5456}(105, \cdot)\) None 0 8
5456.2.hs \(\chi_{5456}(391, \cdot)\) None 0 8
5456.2.hu \(\chi_{5456}(1071, \cdot)\) n/a 1536 8
5456.2.hy \(\chi_{5456}(65, \cdot)\) n/a 1520 8
5456.2.hz \(\chi_{5456}(175, \cdot)\) n/a 1536 8
5456.2.ib \(\chi_{5456}(361, \cdot)\) None 0 8
5456.2.ie \(\chi_{5456}(455, \cdot)\) None 0 8
5456.2.ig \(\chi_{5456}(119, \cdot)\) None 0 8
5456.2.ii \(\chi_{5456}(487, \cdot)\) None 0 8
5456.2.ij \(\chi_{5456}(25, \cdot)\) None 0 8
5456.2.il \(\chi_{5456}(537, \cdot)\) None 0 8
5456.2.in \(\chi_{5456}(9, \cdot)\) None 0 8
5456.2.iq \(\chi_{5456}(663, \cdot)\) None 0 8
5456.2.is \(\chi_{5456}(255, \cdot)\) n/a 1536 8
5456.2.it \(\chi_{5456}(673, \cdot)\) n/a 1520 8
5456.2.iv \(\chi_{5456}(145, \cdot)\) n/a 1520 8
5456.2.ix \(\chi_{5456}(161, \cdot)\) n/a 1520 8
5456.2.ja \(\chi_{5456}(1135, \cdot)\) n/a 1536 8
5456.2.jc \(\chi_{5456}(831, \cdot)\) n/a 1536 8
5456.2.je \(\chi_{5456}(1311, \cdot)\) n/a 1536 8
5456.2.jf \(\chi_{5456}(17, \cdot)\) n/a 1520 8
5456.2.jh \(\chi_{5456}(199, \cdot)\) None 0 8
5456.2.jk \(\chi_{5456}(441, \cdot)\) None 0 8
5456.2.jm \(\chi_{5456}(1695, \cdot)\) n/a 1280 8
5456.2.jo \(\chi_{5456}(183, \cdot)\) None 0 8
5456.2.jr \(\chi_{5456}(73, \cdot)\) None 0 8
5456.2.jt \(\chi_{5456}(57, \cdot)\) None 0 8
5456.2.jv \(\chi_{5456}(601, \cdot)\) None 0 8
5456.2.jw \(\chi_{5456}(679, \cdot)\) None 0 8
5456.2.jy \(\chi_{5456}(7, \cdot)\) None 0 8
5456.2.ka \(\chi_{5456}(1575, \cdot)\) None 0 8
5456.2.kd \(\chi_{5456}(393, \cdot)\) None 0 8
5456.2.kf \(\chi_{5456}(223, \cdot)\) n/a 1536 8
5456.2.kh \(\chi_{5456}(207, \cdot)\) n/a 1536 8
5456.2.kj \(\chi_{5456}(735, \cdot)\) n/a 1536 8
5456.2.ko \(\chi_{5456}(383, \cdot)\) n/a 1536 8
5456.2.kq \(\chi_{5456}(1385, \cdot)\) None 0 8
5456.2.kt \(\chi_{5456}(1495, \cdot)\) None 0 8
5456.2.kv \(\chi_{5456}(135, \cdot)\) None 0 8
5456.2.kw \(\chi_{5456}(169, \cdot)\) None 0 8
5456.2.ky \(\chi_{5456}(513, \cdot)\) n/a 1520 8
5456.2.lb \(\chi_{5456}(431, \cdot)\) n/a 1536 8
5456.2.lc \(\chi_{5456}(115, \cdot)\) n/a 12224 16
5456.2.lf \(\chi_{5456}(365, \cdot)\) n/a 12224 16
5456.2.lg \(\chi_{5456}(51, \cdot)\) n/a 12224 16
5456.2.li \(\chi_{5456}(5, \cdot)\) n/a 12224 16
5456.2.lk \(\chi_{5456}(245, \cdot)\) n/a 12224 16
5456.2.lm \(\chi_{5456}(45, \cdot)\) n/a 10240 16
5456.2.lp \(\chi_{5456}(227, \cdot)\) n/a 12224 16
5456.2.lr \(\chi_{5456}(131, \cdot)\) n/a 12224 16
5456.2.lt \(\chi_{5456}(211, \cdot)\) n/a 12224 16
5456.2.lv \(\chi_{5456}(565, \cdot)\) n/a 12224 16
5456.2.lw \(\chi_{5456}(69, \cdot)\) n/a 12224 16
5456.2.lz \(\chi_{5456}(547, \cdot)\) n/a 12224 16
5456.2.ma \(\chi_{5456}(117, \cdot)\) n/a 12224 16
5456.2.mc \(\chi_{5456}(1235, \cdot)\) n/a 12224 16
5456.2.me \(\chi_{5456}(3, \cdot)\) n/a 12224 16
5456.2.mg \(\chi_{5456}(331, \cdot)\) n/a 10240 16
5456.2.mj \(\chi_{5456}(261, \cdot)\) n/a 12224 16
5456.2.ml \(\chi_{5456}(21, \cdot)\) n/a 12224 16
5456.2.mn \(\chi_{5456}(677, \cdot)\) n/a 12224 16
5456.2.mp \(\chi_{5456}(675, \cdot)\) n/a 12224 16
5456.2.mq \(\chi_{5456}(75, \cdot)\) n/a 12224 16
5456.2.mt \(\chi_{5456}(13, \cdot)\) n/a 12224 16
5456.2.mu \(\chi_{5456}(317, \cdot)\) n/a 12224 16
5456.2.mx \(\chi_{5456}(19, \cdot)\) n/a 12224 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5456))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5456)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(248))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(341))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(496))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(682))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1364))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5456))\)\(^{\oplus 1}\)