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Properties

Label 5712.2
Level 5712
Weight 2
Dimension 353864
Nonzero newspaces 104
Sturm bound 3538944

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Defining parameters

Level: \( N \) = \( 5712 = 2^{4} \cdot 3 \cdot 7 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 104 \)
Sturm bound: \(3538944\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5712))\).

Total New Old
Modular forms 895488 356560 538928
Cusp forms 873985 353864 520121
Eisenstein series 21503 2696 18807

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5712))\)

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
5712.2.a \(\chi_{5712}(1, \cdot)\) 5712.2.a.a 1 1
5712.2.a.b 1
5712.2.a.c 1
5712.2.a.d 1
5712.2.a.e 1
5712.2.a.f 1
5712.2.a.g 1
5712.2.a.h 1
5712.2.a.i 1
5712.2.a.j 1
5712.2.a.k 1
5712.2.a.l 1
5712.2.a.m 1
5712.2.a.n 1
5712.2.a.o 1
5712.2.a.p 1
5712.2.a.q 1
5712.2.a.r 1
5712.2.a.s 1
5712.2.a.t 1
5712.2.a.u 1
5712.2.a.v 1
5712.2.a.w 1
5712.2.a.x 1
5712.2.a.y 1
5712.2.a.z 1
5712.2.a.ba 1
5712.2.a.bb 1
5712.2.a.bc 2
5712.2.a.bd 2
5712.2.a.be 2
5712.2.a.bf 2
5712.2.a.bg 2
5712.2.a.bh 2
5712.2.a.bi 2
5712.2.a.bj 2
5712.2.a.bk 2
5712.2.a.bl 2
5712.2.a.bm 2
5712.2.a.bn 2
5712.2.a.bo 2
5712.2.a.bp 2
5712.2.a.bq 2
5712.2.a.br 2
5712.2.a.bs 3
5712.2.a.bt 3
5712.2.a.bu 3
5712.2.a.bv 3
5712.2.a.bw 3
5712.2.a.bx 4
5712.2.a.by 4
5712.2.a.bz 4
5712.2.a.ca 4
5712.2.a.cb 5
5712.2.c \(\chi_{5712}(2857, \cdot)\) None 0 1
5712.2.e \(\chi_{5712}(4591, \cdot)\) n/a 128 1
5712.2.f \(\chi_{5712}(4759, \cdot)\) None 0 1
5712.2.h \(\chi_{5712}(3025, \cdot)\) n/a 108 1
5712.2.k \(\chi_{5712}(3569, \cdot)\) n/a 284 1
5712.2.m \(\chi_{5712}(407, \cdot)\) None 0 1
5712.2.n \(\chi_{5712}(239, \cdot)\) n/a 192 1
5712.2.p \(\chi_{5712}(3401, \cdot)\) None 0 1
5712.2.r \(\chi_{5712}(545, \cdot)\) n/a 256 1
5712.2.t \(\chi_{5712}(3095, \cdot)\) None 0 1
5712.2.w \(\chi_{5712}(3263, \cdot)\) n/a 216 1
5712.2.y \(\chi_{5712}(713, \cdot)\) None 0 1
5712.2.z \(\chi_{5712}(169, \cdot)\) None 0 1
5712.2.bb \(\chi_{5712}(1903, \cdot)\) n/a 144 1
5712.2.be \(\chi_{5712}(1735, \cdot)\) None 0 1
5712.2.bg \(\chi_{5712}(1633, \cdot)\) n/a 256 2
5712.2.bh \(\chi_{5712}(965, \cdot)\) n/a 2288 2
5712.2.bk \(\chi_{5712}(659, \cdot)\) n/a 1728 2
5712.2.bm \(\chi_{5712}(1483, \cdot)\) n/a 1152 2
5712.2.bn \(\chi_{5712}(421, \cdot)\) n/a 864 2
5712.2.bq \(\chi_{5712}(1415, \cdot)\) None 0 2
5712.2.bs \(\chi_{5712}(2911, \cdot)\) n/a 288 2
5712.2.bu \(\chi_{5712}(4577, \cdot)\) n/a 568 2
5712.2.bw \(\chi_{5712}(1177, \cdot)\) None 0 2
5712.2.by \(\chi_{5712}(475, \cdot)\) n/a 1152 2
5712.2.ca \(\chi_{5712}(1667, \cdot)\) n/a 1536 2
5712.2.cc \(\chi_{5712}(1429, \cdot)\) n/a 768 2
5712.2.ce \(\chi_{5712}(2141, \cdot)\) n/a 2288 2
5712.2.cg \(\chi_{5712}(1973, \cdot)\) n/a 2048 2
5712.2.ci \(\chi_{5712}(1597, \cdot)\) n/a 864 2
5712.2.ck \(\chi_{5712}(1835, \cdot)\) n/a 1728 2
5712.2.cm \(\chi_{5712}(307, \cdot)\) n/a 1024 2
5712.2.co \(\chi_{5712}(4033, \cdot)\) n/a 216 2
5712.2.cq \(\chi_{5712}(1721, \cdot)\) None 0 2
5712.2.cs \(\chi_{5712}(55, \cdot)\) None 0 2
5712.2.cu \(\chi_{5712}(4271, \cdot)\) n/a 432 2
5712.2.cw \(\chi_{5712}(3277, \cdot)\) n/a 864 2
5712.2.cx \(\chi_{5712}(2155, \cdot)\) n/a 1152 2
5712.2.cz \(\chi_{5712}(3515, \cdot)\) n/a 1728 2
5712.2.dc \(\chi_{5712}(293, \cdot)\) n/a 2288 2
5712.2.de \(\chi_{5712}(271, \cdot)\) n/a 288 2
5712.2.dg \(\chi_{5712}(1801, \cdot)\) None 0 2
5712.2.di \(\chi_{5712}(103, \cdot)\) None 0 2
5712.2.dl \(\chi_{5712}(2279, \cdot)\) None 0 2
5712.2.dn \(\chi_{5712}(1361, \cdot)\) n/a 512 2
5712.2.do \(\chi_{5712}(1529, \cdot)\) None 0 2
5712.2.dq \(\chi_{5712}(2447, \cdot)\) n/a 576 2
5712.2.ds \(\chi_{5712}(2039, \cdot)\) None 0 2
5712.2.du \(\chi_{5712}(1937, \cdot)\) n/a 568 2
5712.2.dx \(\chi_{5712}(1769, \cdot)\) None 0 2
5712.2.dz \(\chi_{5712}(1871, \cdot)\) n/a 512 2
5712.2.ea \(\chi_{5712}(2959, \cdot)\) n/a 256 2
5712.2.ec \(\chi_{5712}(2041, \cdot)\) None 0 2
5712.2.ef \(\chi_{5712}(2209, \cdot)\) n/a 288 2
5712.2.eh \(\chi_{5712}(3127, \cdot)\) None 0 2
5712.2.ei \(\chi_{5712}(1345, \cdot)\) n/a 432 4
5712.2.ej \(\chi_{5712}(1063, \cdot)\) None 0 4
5712.2.ek \(\chi_{5712}(1385, \cdot)\) None 0 4
5712.2.el \(\chi_{5712}(1583, \cdot)\) n/a 864 4
5712.2.eq \(\chi_{5712}(155, \cdot)\) n/a 3456 4
5712.2.er \(\chi_{5712}(253, \cdot)\) n/a 1728 4
5712.2.eu \(\chi_{5712}(2813, \cdot)\) n/a 4576 4
5712.2.ev \(\chi_{5712}(1147, \cdot)\) n/a 2304 4
5712.2.ey \(\chi_{5712}(461, \cdot)\) n/a 4576 4
5712.2.ez \(\chi_{5712}(4003, \cdot)\) n/a 2304 4
5712.2.fc \(\chi_{5712}(2507, \cdot)\) n/a 3456 4
5712.2.fd \(\chi_{5712}(2269, \cdot)\) n/a 1728 4
5712.2.fg \(\chi_{5712}(841, \cdot)\) None 0 4
5712.2.fh \(\chi_{5712}(223, \cdot)\) n/a 576 4
5712.2.fi \(\chi_{5712}(1889, \cdot)\) n/a 1136 4
5712.2.fj \(\chi_{5712}(1079, \cdot)\) None 0 4
5712.2.fp \(\chi_{5712}(1619, \cdot)\) n/a 4576 4
5712.2.fq \(\chi_{5712}(1109, \cdot)\) n/a 4576 4
5712.2.fs \(\chi_{5712}(1381, \cdot)\) n/a 2304 4
5712.2.fv \(\chi_{5712}(523, \cdot)\) n/a 2304 4
5712.2.fw \(\chi_{5712}(353, \cdot)\) n/a 1136 4
5712.2.fy \(\chi_{5712}(361, \cdot)\) None 0 4
5712.2.ga \(\chi_{5712}(599, \cdot)\) None 0 4
5712.2.gc \(\chi_{5712}(1279, \cdot)\) n/a 576 4
5712.2.ge \(\chi_{5712}(611, \cdot)\) n/a 4576 4
5712.2.gg \(\chi_{5712}(1123, \cdot)\) n/a 2048 4
5712.2.gi \(\chi_{5712}(341, \cdot)\) n/a 4096 4
5712.2.gk \(\chi_{5712}(373, \cdot)\) n/a 2304 4
5712.2.gm \(\chi_{5712}(205, \cdot)\) n/a 2048 4
5712.2.go \(\chi_{5712}(101, \cdot)\) n/a 4576 4
5712.2.gq \(\chi_{5712}(1291, \cdot)\) n/a 2304 4
5712.2.gs \(\chi_{5712}(443, \cdot)\) n/a 4096 4
5712.2.gu \(\chi_{5712}(871, \cdot)\) None 0 4
5712.2.gw \(\chi_{5712}(191, \cdot)\) n/a 1152 4
5712.2.gy \(\chi_{5712}(625, \cdot)\) n/a 576 4
5712.2.ha \(\chi_{5712}(89, \cdot)\) None 0 4
5712.2.hc \(\chi_{5712}(115, \cdot)\) n/a 2304 4
5712.2.hf \(\chi_{5712}(1789, \cdot)\) n/a 2304 4
5712.2.hh \(\chi_{5712}(1517, \cdot)\) n/a 4576 4
5712.2.hi \(\chi_{5712}(2027, \cdot)\) n/a 4576 4
5712.2.hl \(\chi_{5712}(29, \cdot)\) n/a 6912 8
5712.2.hn \(\chi_{5712}(419, \cdot)\) n/a 9152 8
5712.2.ho \(\chi_{5712}(853, \cdot)\) n/a 4608 8
5712.2.hq \(\chi_{5712}(547, \cdot)\) n/a 3456 8
5712.2.hw \(\chi_{5712}(295, \cdot)\) None 0 8
5712.2.hx \(\chi_{5712}(97, \cdot)\) n/a 1152 8
5712.2.hy \(\chi_{5712}(167, \cdot)\) None 0 8
5712.2.hz \(\chi_{5712}(113, \cdot)\) n/a 1728 8
5712.2.ia \(\chi_{5712}(265, \cdot)\) None 0 8
5712.2.ib \(\chi_{5712}(1807, \cdot)\) n/a 864 8
5712.2.ic \(\chi_{5712}(617, \cdot)\) None 0 8
5712.2.id \(\chi_{5712}(335, \cdot)\) n/a 2304 8
5712.2.ij \(\chi_{5712}(1091, \cdot)\) n/a 9152 8
5712.2.il \(\chi_{5712}(2213, \cdot)\) n/a 6912 8
5712.2.im \(\chi_{5712}(211, \cdot)\) n/a 3456 8
5712.2.io \(\chi_{5712}(181, \cdot)\) n/a 4608 8
5712.2.iu \(\chi_{5712}(535, \cdot)\) None 0 8
5712.2.iv \(\chi_{5712}(529, \cdot)\) n/a 1152 8
5712.2.iw \(\chi_{5712}(767, \cdot)\) n/a 2304 8
5712.2.ix \(\chi_{5712}(185, \cdot)\) None 0 8
5712.2.ja \(\chi_{5712}(773, \cdot)\) n/a 9152 8
5712.2.jb \(\chi_{5712}(451, \cdot)\) n/a 4608 8
5712.2.je \(\chi_{5712}(1691, \cdot)\) n/a 9152 8
5712.2.jf \(\chi_{5712}(1453, \cdot)\) n/a 4608 8
5712.2.ji \(\chi_{5712}(179, \cdot)\) n/a 9152 8
5712.2.jj \(\chi_{5712}(1045, \cdot)\) n/a 4608 8
5712.2.jm \(\chi_{5712}(1181, \cdot)\) n/a 9152 8
5712.2.jn \(\chi_{5712}(19, \cdot)\) n/a 4608 8
5712.2.js \(\chi_{5712}(943, \cdot)\) n/a 1152 8
5712.2.jt \(\chi_{5712}(25, \cdot)\) None 0 8
5712.2.ju \(\chi_{5712}(263, \cdot)\) None 0 8
5712.2.jv \(\chi_{5712}(257, \cdot)\) n/a 2272 8
5712.2.jx \(\chi_{5712}(403, \cdot)\) n/a 9216 16
5712.2.jz \(\chi_{5712}(61, \cdot)\) n/a 9216 16
5712.2.ka \(\chi_{5712}(227, \cdot)\) n/a 18304 16
5712.2.kc \(\chi_{5712}(725, \cdot)\) n/a 18304 16
5712.2.ki \(\chi_{5712}(143, \cdot)\) n/a 4608 16
5712.2.kj \(\chi_{5712}(233, \cdot)\) None 0 16
5712.2.kk \(\chi_{5712}(79, \cdot)\) n/a 2304 16
5712.2.kl \(\chi_{5712}(73, \cdot)\) None 0 16
5712.2.km \(\chi_{5712}(65, \cdot)\) n/a 4544 16
5712.2.kn \(\chi_{5712}(215, \cdot)\) None 0 16
5712.2.ko \(\chi_{5712}(241, \cdot)\) n/a 2304 16
5712.2.kp \(\chi_{5712}(487, \cdot)\) None 0 16
5712.2.kv \(\chi_{5712}(997, \cdot)\) n/a 9216 16
5712.2.kx \(\chi_{5712}(163, \cdot)\) n/a 9216 16
5712.2.ky \(\chi_{5712}(317, \cdot)\) n/a 18304 16
5712.2.la \(\chi_{5712}(131, \cdot)\) n/a 18304 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5712))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5712)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(357))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(408))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(476))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(714))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(816))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(952))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1428))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1904))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2856))\)\(^{\oplus 2}\)