Properties

Label 2352.2
Level 2352
Weight 2
Dimension 60503
Nonzero newspaces 32
Sturm bound 602112
Trace bound 9

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Defining parameters

Level: \( N \) = \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(602112\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2352))\).

Total New Old
Modular forms 153888 61375 92513
Cusp forms 147169 60503 86666
Eisenstein series 6719 872 5847

Trace form

\( 60503q - 46q^{3} - 128q^{4} - 2q^{5} - 68q^{6} - 108q^{7} - 12q^{8} - 20q^{9} + O(q^{10}) \) \( 60503q - 46q^{3} - 128q^{4} - 2q^{5} - 68q^{6} - 108q^{7} - 12q^{8} - 20q^{9} - 128q^{10} - 12q^{11} - 60q^{12} - 172q^{13} - 91q^{15} - 104q^{16} + 2q^{17} - 52q^{18} - 130q^{19} + 16q^{20} - 102q^{21} - 200q^{22} - 64q^{23} - 32q^{24} - 117q^{25} + 20q^{26} - 40q^{27} - 144q^{28} - 58q^{29} - 40q^{30} - 170q^{31} - 191q^{33} - 128q^{34} - 36q^{35} - 92q^{36} - 232q^{37} - 8q^{38} - 21q^{39} - 144q^{40} - 6q^{41} - 138q^{43} + 152q^{44} + 7q^{45} + 72q^{46} + 72q^{47} + 116q^{48} - 228q^{49} + 300q^{50} + 49q^{51} + 280q^{52} + 206q^{53} + 228q^{54} + 98q^{55} + 168q^{56} + 157q^{57} + 232q^{58} + 124q^{59} + 284q^{60} + 96q^{61} + 420q^{62} - 24q^{63} + 184q^{64} + 180q^{65} + 232q^{66} - 2q^{67} + 272q^{68} + 91q^{69} - 48q^{70} + 16q^{71} + 168q^{72} + 52q^{74} + 74q^{75} - 56q^{76} - 60q^{78} - 106q^{79} + 8q^{80} - 32q^{81} - 96q^{82} - 36q^{83} - 72q^{84} - 258q^{85} - 16q^{86} + 27q^{87} - 152q^{88} - 6q^{89} - 84q^{90} + 102q^{91} - 64q^{92} + 29q^{93} - 448q^{94} + 304q^{95} - 356q^{96} - 274q^{97} - 168q^{98} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2352))\)

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
2352.2.a \(\chi_{2352}(1, \cdot)\) 2352.2.a.a 1 1
2352.2.a.b 1
2352.2.a.c 1
2352.2.a.d 1
2352.2.a.e 1
2352.2.a.f 1
2352.2.a.g 1
2352.2.a.h 1
2352.2.a.i 1
2352.2.a.j 1
2352.2.a.k 1
2352.2.a.l 1
2352.2.a.m 1
2352.2.a.n 1
2352.2.a.o 1
2352.2.a.p 1
2352.2.a.q 1
2352.2.a.r 1
2352.2.a.s 1
2352.2.a.t 1
2352.2.a.u 1
2352.2.a.v 1
2352.2.a.w 1
2352.2.a.x 1
2352.2.a.y 1
2352.2.a.z 2
2352.2.a.ba 2
2352.2.a.bb 2
2352.2.a.bc 2
2352.2.a.bd 2
2352.2.a.be 2
2352.2.a.bf 2
2352.2.a.bg 2
2352.2.b \(\chi_{2352}(1567, \cdot)\) 2352.2.b.a 2 1
2352.2.b.b 2
2352.2.b.c 2
2352.2.b.d 2
2352.2.b.e 2
2352.2.b.f 2
2352.2.b.g 2
2352.2.b.h 2
2352.2.b.i 4
2352.2.b.j 4
2352.2.b.k 8
2352.2.b.l 8
2352.2.c \(\chi_{2352}(1177, \cdot)\) None 0 1
2352.2.h \(\chi_{2352}(2255, \cdot)\) 2352.2.h.a 2 1
2352.2.h.b 2
2352.2.h.c 2
2352.2.h.d 2
2352.2.h.e 2
2352.2.h.f 4
2352.2.h.g 4
2352.2.h.h 4
2352.2.h.i 4
2352.2.h.j 4
2352.2.h.k 4
2352.2.h.l 8
2352.2.h.m 8
2352.2.h.n 8
2352.2.h.o 8
2352.2.h.p 16
2352.2.i \(\chi_{2352}(2057, \cdot)\) None 0 1
2352.2.j \(\chi_{2352}(1079, \cdot)\) None 0 1
2352.2.k \(\chi_{2352}(881, \cdot)\) 2352.2.k.a 2 1
2352.2.k.b 2
2352.2.k.c 2
2352.2.k.d 2
2352.2.k.e 4
2352.2.k.f 8
2352.2.k.g 8
2352.2.k.h 8
2352.2.k.i 16
2352.2.k.j 24
2352.2.p \(\chi_{2352}(391, \cdot)\) None 0 1
2352.2.q \(\chi_{2352}(961, \cdot)\) 2352.2.q.a 2 2
2352.2.q.b 2
2352.2.q.c 2
2352.2.q.d 2
2352.2.q.e 2
2352.2.q.f 2
2352.2.q.g 2
2352.2.q.h 2
2352.2.q.i 2
2352.2.q.j 2
2352.2.q.k 2
2352.2.q.l 2
2352.2.q.m 2
2352.2.q.n 2
2352.2.q.o 2
2352.2.q.p 2
2352.2.q.q 2
2352.2.q.r 2
2352.2.q.s 2
2352.2.q.t 2
2352.2.q.u 2
2352.2.q.v 2
2352.2.q.w 2
2352.2.q.x 2
2352.2.q.y 2
2352.2.q.z 2
2352.2.q.ba 4
2352.2.q.bb 4
2352.2.q.bc 4
2352.2.q.bd 4
2352.2.q.be 4
2352.2.q.bf 4
2352.2.q.bg 4
2352.2.s \(\chi_{2352}(491, \cdot)\) n/a 636 2
2352.2.u \(\chi_{2352}(979, \cdot)\) n/a 320 2
2352.2.w \(\chi_{2352}(589, \cdot)\) n/a 328 2
2352.2.y \(\chi_{2352}(293, \cdot)\) n/a 624 2
2352.2.bb \(\chi_{2352}(1207, \cdot)\) None 0 2
2352.2.bc \(\chi_{2352}(1697, \cdot)\) n/a 152 2
2352.2.bd \(\chi_{2352}(263, \cdot)\) None 0 2
2352.2.bi \(\chi_{2352}(521, \cdot)\) None 0 2
2352.2.bj \(\chi_{2352}(863, \cdot)\) n/a 160 2
2352.2.bk \(\chi_{2352}(361, \cdot)\) None 0 2
2352.2.bl \(\chi_{2352}(31, \cdot)\) 2352.2.bl.a 2 2
2352.2.bl.b 2
2352.2.bl.c 2
2352.2.bl.d 2
2352.2.bl.e 2
2352.2.bl.f 2
2352.2.bl.g 2
2352.2.bl.h 2
2352.2.bl.i 2
2352.2.bl.j 2
2352.2.bl.k 2
2352.2.bl.l 2
2352.2.bl.m 4
2352.2.bl.n 4
2352.2.bl.o 8
2352.2.bl.p 8
2352.2.bl.q 8
2352.2.bl.r 8
2352.2.bl.s 8
2352.2.bl.t 8
2352.2.bo \(\chi_{2352}(337, \cdot)\) n/a 336 6
2352.2.bp \(\chi_{2352}(509, \cdot)\) n/a 1248 4
2352.2.br \(\chi_{2352}(373, \cdot)\) n/a 640 4
2352.2.bt \(\chi_{2352}(19, \cdot)\) n/a 640 4
2352.2.bv \(\chi_{2352}(275, \cdot)\) n/a 1248 4
2352.2.bx \(\chi_{2352}(55, \cdot)\) None 0 6
2352.2.cc \(\chi_{2352}(209, \cdot)\) n/a 660 6
2352.2.cd \(\chi_{2352}(71, \cdot)\) None 0 6
2352.2.ce \(\chi_{2352}(41, \cdot)\) None 0 6
2352.2.cf \(\chi_{2352}(239, \cdot)\) n/a 672 6
2352.2.ck \(\chi_{2352}(169, \cdot)\) None 0 6
2352.2.cl \(\chi_{2352}(223, \cdot)\) n/a 336 6
2352.2.cm \(\chi_{2352}(193, \cdot)\) n/a 672 12
2352.2.cn \(\chi_{2352}(125, \cdot)\) n/a 5328 12
2352.2.cp \(\chi_{2352}(85, \cdot)\) n/a 2688 12
2352.2.cr \(\chi_{2352}(139, \cdot)\) n/a 2688 12
2352.2.ct \(\chi_{2352}(155, \cdot)\) n/a 5328 12
2352.2.cx \(\chi_{2352}(271, \cdot)\) n/a 672 12
2352.2.cy \(\chi_{2352}(25, \cdot)\) None 0 12
2352.2.cz \(\chi_{2352}(95, \cdot)\) n/a 1344 12
2352.2.da \(\chi_{2352}(89, \cdot)\) None 0 12
2352.2.df \(\chi_{2352}(23, \cdot)\) None 0 12
2352.2.dg \(\chi_{2352}(17, \cdot)\) n/a 1320 12
2352.2.dh \(\chi_{2352}(103, \cdot)\) None 0 12
2352.2.dl \(\chi_{2352}(11, \cdot)\) n/a 10656 24
2352.2.dn \(\chi_{2352}(115, \cdot)\) n/a 5376 24
2352.2.dp \(\chi_{2352}(37, \cdot)\) n/a 5376 24
2352.2.dr \(\chi_{2352}(5, \cdot)\) n/a 10656 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2352))\) into lower level spaces

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