Properties

Label 2352.4
Level 2352
Weight 4
Dimension 182381
Nonzero newspaces 32
Sturm bound 1204224
Trace bound 9

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Defining parameters

Level: \( N \) = \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(1204224\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2352))\).

Total New Old
Modular forms 454944 183253 271691
Cusp forms 448224 182381 265843
Eisenstein series 6720 872 5848

Trace form

\( 182381q - 50q^{3} - 144q^{4} + 2q^{5} - 32q^{6} - 108q^{7} + 84q^{8} + 42q^{9} + O(q^{10}) \) \( 182381q - 50q^{3} - 144q^{4} + 2q^{5} - 32q^{6} - 108q^{7} + 84q^{8} + 42q^{9} + 8q^{10} - 60q^{11} - 164q^{12} - 176q^{13} + 69q^{15} - 424q^{16} - 26q^{17} - 44q^{18} - 1138q^{19} + 80q^{20} - 270q^{21} + 448q^{22} + 256q^{23} + 48q^{24} + 1765q^{25} - 20q^{26} + 124q^{27} - 144q^{28} + 1258q^{29} - 800q^{30} + 630q^{31} - 960q^{32} + 281q^{33} - 304q^{34} - 1044q^{35} - 604q^{36} - 2060q^{37} + 1256q^{38} - 181q^{39} + 2256q^{40} + 414q^{41} + 2520q^{42} + 2662q^{43} + 14584q^{44} + 3819q^{45} + 7512q^{46} + 648q^{47} + 852q^{48} - 1572q^{49} - 7692q^{50} - 2727q^{51} - 17368q^{52} - 8174q^{53} - 16168q^{54} - 4062q^{55} - 9240q^{56} - 7923q^{57} - 15072q^{58} - 4756q^{59} - 12244q^{60} - 5636q^{61} - 6612q^{62} - 24q^{63} + 3384q^{64} + 7068q^{65} + 11104q^{66} + 782q^{67} + 22672q^{68} + 14011q^{69} + 14736q^{70} + 3152q^{71} + 7912q^{72} - 4852q^{73} - 2740q^{74} + 998q^{75} - 2568q^{76} - 3348q^{78} + 5942q^{79} + 712q^{80} - 7162q^{81} + 608q^{82} + 5868q^{83} - 72q^{84} + 4902q^{85} - 1712q^{86} - 5061q^{87} + 4808q^{88} - 66q^{89} + 3260q^{90} + 10182q^{91} - 7616q^{92} + 3109q^{93} - 45392q^{94} + 47024q^{95} - 20132q^{96} - 902q^{97} - 11928q^{98} + 17216q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2352))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2352.4.a \(\chi_{2352}(1, \cdot)\) 2352.4.a.a 1 1
2352.4.a.b 1
2352.4.a.c 1
2352.4.a.d 1
2352.4.a.e 1
2352.4.a.f 1
2352.4.a.g 1
2352.4.a.h 1
2352.4.a.i 1
2352.4.a.j 1
2352.4.a.k 1
2352.4.a.l 1
2352.4.a.m 1
2352.4.a.n 1
2352.4.a.o 1
2352.4.a.p 1
2352.4.a.q 1
2352.4.a.r 1
2352.4.a.s 1
2352.4.a.t 1
2352.4.a.u 1
2352.4.a.v 1
2352.4.a.w 1
2352.4.a.x 1
2352.4.a.y 1
2352.4.a.z 1
2352.4.a.ba 1
2352.4.a.bb 1
2352.4.a.bc 1
2352.4.a.bd 1
2352.4.a.be 1
2352.4.a.bf 1
2352.4.a.bg 1
2352.4.a.bh 1
2352.4.a.bi 1
2352.4.a.bj 1
2352.4.a.bk 1
2352.4.a.bl 2
2352.4.a.bm 2
2352.4.a.bn 2
2352.4.a.bo 2
2352.4.a.bp 2
2352.4.a.bq 2
2352.4.a.br 2
2352.4.a.bs 2
2352.4.a.bt 2
2352.4.a.bu 2
2352.4.a.bv 2
2352.4.a.bw 2
2352.4.a.bx 2
2352.4.a.by 2
2352.4.a.bz 2
2352.4.a.ca 2
2352.4.a.cb 2
2352.4.a.cc 2
2352.4.a.cd 2
2352.4.a.ce 2
2352.4.a.cf 2
2352.4.a.cg 3
2352.4.a.ch 3
2352.4.a.ci 3
2352.4.a.cj 3
2352.4.a.ck 4
2352.4.a.cl 4
2352.4.a.cm 4
2352.4.a.cn 4
2352.4.a.co 4
2352.4.a.cp 4
2352.4.a.cq 4
2352.4.a.cr 4
2352.4.b \(\chi_{2352}(1567, \cdot)\) n/a 120 1
2352.4.c \(\chi_{2352}(1177, \cdot)\) None 0 1
2352.4.h \(\chi_{2352}(2255, \cdot)\) n/a 246 1
2352.4.i \(\chi_{2352}(2057, \cdot)\) None 0 1
2352.4.j \(\chi_{2352}(1079, \cdot)\) None 0 1
2352.4.k \(\chi_{2352}(881, \cdot)\) n/a 236 1
2352.4.p \(\chi_{2352}(391, \cdot)\) None 0 1
2352.4.q \(\chi_{2352}(961, \cdot)\) n/a 240 2
2352.4.s \(\chi_{2352}(491, \cdot)\) n/a 1948 2
2352.4.u \(\chi_{2352}(979, \cdot)\) n/a 960 2
2352.4.w \(\chi_{2352}(589, \cdot)\) n/a 984 2
2352.4.y \(\chi_{2352}(293, \cdot)\) n/a 1904 2
2352.4.bb \(\chi_{2352}(1207, \cdot)\) None 0 2
2352.4.bc \(\chi_{2352}(1697, \cdot)\) n/a 472 2
2352.4.bd \(\chi_{2352}(263, \cdot)\) None 0 2
2352.4.bi \(\chi_{2352}(521, \cdot)\) None 0 2
2352.4.bj \(\chi_{2352}(863, \cdot)\) n/a 480 2
2352.4.bk \(\chi_{2352}(361, \cdot)\) None 0 2
2352.4.bl \(\chi_{2352}(31, \cdot)\) n/a 240 2
2352.4.bo \(\chi_{2352}(337, \cdot)\) n/a 1008 6
2352.4.bp \(\chi_{2352}(509, \cdot)\) n/a 3808 4
2352.4.br \(\chi_{2352}(373, \cdot)\) n/a 1920 4
2352.4.bt \(\chi_{2352}(19, \cdot)\) n/a 1920 4
2352.4.bv \(\chi_{2352}(275, \cdot)\) n/a 3808 4
2352.4.bx \(\chi_{2352}(55, \cdot)\) None 0 6
2352.4.cc \(\chi_{2352}(209, \cdot)\) n/a 2004 6
2352.4.cd \(\chi_{2352}(71, \cdot)\) None 0 6
2352.4.ce \(\chi_{2352}(41, \cdot)\) None 0 6
2352.4.cf \(\chi_{2352}(239, \cdot)\) n/a 2016 6
2352.4.ck \(\chi_{2352}(169, \cdot)\) None 0 6
2352.4.cl \(\chi_{2352}(223, \cdot)\) n/a 1008 6
2352.4.cm \(\chi_{2352}(193, \cdot)\) n/a 2016 12
2352.4.cn \(\chi_{2352}(125, \cdot)\) n/a 16080 12
2352.4.cp \(\chi_{2352}(85, \cdot)\) n/a 8064 12
2352.4.cr \(\chi_{2352}(139, \cdot)\) n/a 8064 12
2352.4.ct \(\chi_{2352}(155, \cdot)\) n/a 16080 12
2352.4.cx \(\chi_{2352}(271, \cdot)\) n/a 2016 12
2352.4.cy \(\chi_{2352}(25, \cdot)\) None 0 12
2352.4.cz \(\chi_{2352}(95, \cdot)\) n/a 4032 12
2352.4.da \(\chi_{2352}(89, \cdot)\) None 0 12
2352.4.df \(\chi_{2352}(23, \cdot)\) None 0 12
2352.4.dg \(\chi_{2352}(17, \cdot)\) n/a 4008 12
2352.4.dh \(\chi_{2352}(103, \cdot)\) None 0 12
2352.4.dl \(\chi_{2352}(11, \cdot)\) n/a 32160 24
2352.4.dn \(\chi_{2352}(115, \cdot)\) n/a 16128 24
2352.4.dp \(\chi_{2352}(37, \cdot)\) n/a 16128 24
2352.4.dr \(\chi_{2352}(5, \cdot)\) n/a 32160 24

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2352))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2352)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1176))\)\(^{\oplus 2}\)