Properties

Label 1596.2
Level 1596
Weight 2
Dimension 28476
Nonzero newspaces 64
Sturm bound 276480
Trace bound 25

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Defining parameters

Level: \( N \) = \( 1596 = 2^{2} \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(276480\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1596))\).

Total New Old
Modular forms 71280 29164 42116
Cusp forms 66961 28476 38485
Eisenstein series 4319 688 3631

Trace form

\( 28476 q - 2 q^{3} - 60 q^{4} - 12 q^{5} - 24 q^{6} - 16 q^{7} + 12 q^{8} - 50 q^{9} + O(q^{10}) \) \( 28476 q - 2 q^{3} - 60 q^{4} - 12 q^{5} - 24 q^{6} - 16 q^{7} + 12 q^{8} - 50 q^{9} - 24 q^{10} + 12 q^{11} - 124 q^{13} + 48 q^{14} - 12 q^{16} - 12 q^{17} + 18 q^{18} - 68 q^{19} - 41 q^{21} - 204 q^{22} - 12 q^{23} - 48 q^{24} - 132 q^{25} - 60 q^{26} + 16 q^{27} - 120 q^{28} + 144 q^{29} + 30 q^{30} + 80 q^{31} + 120 q^{32} + 30 q^{33} + 60 q^{34} + 60 q^{35} + 30 q^{36} + 28 q^{37} + 234 q^{38} + 32 q^{39} + 132 q^{40} + 24 q^{41} - 51 q^{42} + 64 q^{43} + 132 q^{44} + 12 q^{45} + 60 q^{46} + 36 q^{47} - 18 q^{48} - 180 q^{49} + 24 q^{50} + 66 q^{51} - 120 q^{52} - 48 q^{53} - 132 q^{54} - 36 q^{56} - 80 q^{57} - 144 q^{58} + 24 q^{59} - 42 q^{60} + 104 q^{61} - 180 q^{62} + 76 q^{63} - 384 q^{64} + 228 q^{65} - 144 q^{66} + 264 q^{67} - 180 q^{68} + 294 q^{69} - 162 q^{70} + 72 q^{71} - 84 q^{72} + 296 q^{73} - 156 q^{74} + 64 q^{75} - 348 q^{76} + 234 q^{77} + 6 q^{78} + 120 q^{79} - 144 q^{80} - 290 q^{81} - 444 q^{82} - 12 q^{83} + 75 q^{84} + 144 q^{85} - 120 q^{86} - 96 q^{87} - 120 q^{88} + 84 q^{89} + 78 q^{90} - 64 q^{91} - 12 q^{92} - 142 q^{93} - 60 q^{94} - 90 q^{95} - 84 q^{96} - 364 q^{97} + 84 q^{98} - 162 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1596))\)

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
1596.2.a \(\chi_{1596}(1, \cdot)\) 1596.2.a.a 1 1
1596.2.a.b 1
1596.2.a.c 1
1596.2.a.d 1
1596.2.a.e 1
1596.2.a.f 2
1596.2.a.g 2
1596.2.a.h 2
1596.2.a.i 2
1596.2.a.j 3
1596.2.b \(\chi_{1596}(113, \cdot)\) 1596.2.b.a 2 1
1596.2.b.b 2
1596.2.b.c 8
1596.2.b.d 12
1596.2.b.e 16
1596.2.c \(\chi_{1596}(1483, \cdot)\) n/a 144 1
1596.2.h \(\chi_{1596}(1331, \cdot)\) n/a 216 1
1596.2.i \(\chi_{1596}(265, \cdot)\) 1596.2.i.a 14 1
1596.2.i.b 14
1596.2.j \(\chi_{1596}(1217, \cdot)\) 1596.2.j.a 48 1
1596.2.k \(\chi_{1596}(379, \cdot)\) n/a 120 1
1596.2.p \(\chi_{1596}(1595, \cdot)\) n/a 312 1
1596.2.q \(\chi_{1596}(961, \cdot)\) 1596.2.q.a 2 2
1596.2.q.b 2
1596.2.q.c 2
1596.2.q.d 2
1596.2.q.e 18
1596.2.q.f 26
1596.2.r \(\chi_{1596}(457, \cdot)\) 1596.2.r.a 2 2
1596.2.r.b 2
1596.2.r.c 2
1596.2.r.d 2
1596.2.r.e 8
1596.2.r.f 8
1596.2.r.g 10
1596.2.r.h 14
1596.2.s \(\chi_{1596}(505, \cdot)\) 1596.2.s.a 2 2
1596.2.s.b 2
1596.2.s.c 8
1596.2.s.d 8
1596.2.s.e 8
1596.2.s.f 12
1596.2.t \(\chi_{1596}(121, \cdot)\) 1596.2.t.a 2 2
1596.2.t.b 2
1596.2.t.c 2
1596.2.t.d 2
1596.2.t.e 18
1596.2.t.f 26
1596.2.u \(\chi_{1596}(145, \cdot)\) 1596.2.u.a 2 2
1596.2.u.b 24
1596.2.u.c 26
1596.2.v \(\chi_{1596}(11, \cdot)\) n/a 624 2
1596.2.ba \(\chi_{1596}(619, \cdot)\) n/a 320 2
1596.2.bb \(\chi_{1596}(905, \cdot)\) n/a 108 2
1596.2.be \(\chi_{1596}(125, \cdot)\) n/a 104 2
1596.2.bf \(\chi_{1596}(715, \cdot)\) n/a 240 2
1596.2.bi \(\chi_{1596}(563, \cdot)\) n/a 624 2
1596.2.bl \(\chi_{1596}(227, \cdot)\) n/a 624 2
1596.2.bm \(\chi_{1596}(151, \cdot)\) n/a 320 2
1596.2.bn \(\chi_{1596}(761, \cdot)\) 1596.2.bn.a 96 2
1596.2.bq \(\chi_{1596}(331, \cdot)\) n/a 320 2
1596.2.br \(\chi_{1596}(1109, \cdot)\) n/a 108 2
1596.2.bu \(\chi_{1596}(335, \cdot)\) n/a 624 2
1596.2.bz \(\chi_{1596}(449, \cdot)\) 1596.2.bz.a 2 2
1596.2.bz.b 2
1596.2.bz.c 4
1596.2.bz.d 16
1596.2.bz.e 24
1596.2.bz.f 32
1596.2.ca \(\chi_{1596}(391, \cdot)\) n/a 320 2
1596.2.cd \(\chi_{1596}(829, \cdot)\) 1596.2.cd.a 2 2
1596.2.cd.b 24
1596.2.cd.c 26
1596.2.ce \(\chi_{1596}(695, \cdot)\) n/a 624 2
1596.2.ch \(\chi_{1596}(493, \cdot)\) 1596.2.ch.a 2 2
1596.2.ch.b 2
1596.2.ch.c 24
1596.2.ch.d 24
1596.2.ci \(\chi_{1596}(191, \cdot)\) n/a 576 2
1596.2.cj \(\chi_{1596}(115, \cdot)\) n/a 288 2
1596.2.ck \(\chi_{1596}(569, \cdot)\) n/a 108 2
1596.2.cn \(\chi_{1596}(1375, \cdot)\) n/a 320 2
1596.2.co \(\chi_{1596}(65, \cdot)\) n/a 108 2
1596.2.cr \(\chi_{1596}(239, \cdot)\) n/a 480 2
1596.2.cs \(\chi_{1596}(601, \cdot)\) 1596.2.cs.a 28 2
1596.2.cs.b 28
1596.2.cv \(\chi_{1596}(1319, \cdot)\) n/a 624 2
1596.2.da \(\chi_{1596}(1171, \cdot)\) n/a 320 2
1596.2.db \(\chi_{1596}(353, \cdot)\) n/a 108 2
1596.2.dc \(\chi_{1596}(85, \cdot)\) n/a 120 6
1596.2.dd \(\chi_{1596}(289, \cdot)\) n/a 162 6
1596.2.de \(\chi_{1596}(25, \cdot)\) n/a 162 6
1596.2.df \(\chi_{1596}(187, \cdot)\) n/a 960 6
1596.2.di \(\chi_{1596}(67, \cdot)\) n/a 960 6
1596.2.dk \(\chi_{1596}(5, \cdot)\) n/a 318 6
1596.2.dl \(\chi_{1596}(53, \cdot)\) n/a 318 6
1596.2.dn \(\chi_{1596}(23, \cdot)\) n/a 1872 6
1596.2.dq \(\chi_{1596}(59, \cdot)\) n/a 1872 6
1596.2.ds \(\chi_{1596}(13, \cdot)\) n/a 156 6
1596.2.du \(\chi_{1596}(167, \cdot)\) n/a 1872 6
1596.2.dx \(\chi_{1596}(491, \cdot)\) n/a 1440 6
1596.2.dz \(\chi_{1596}(325, \cdot)\) n/a 162 6
1596.2.eb \(\chi_{1596}(17, \cdot)\) n/a 318 6
1596.2.ee \(\chi_{1596}(317, \cdot)\) n/a 318 6
1596.2.eg \(\chi_{1596}(127, \cdot)\) n/a 720 6
1596.2.eh \(\chi_{1596}(55, \cdot)\) n/a 960 6
1596.2.ej \(\chi_{1596}(29, \cdot)\) n/a 240 6
1596.2.em \(\chi_{1596}(377, \cdot)\) n/a 324 6
1596.2.eo \(\chi_{1596}(283, \cdot)\) n/a 960 6
1596.2.ep \(\chi_{1596}(583, \cdot)\) n/a 960 6
1596.2.et \(\chi_{1596}(241, \cdot)\) n/a 162 6
1596.2.ev \(\chi_{1596}(359, \cdot)\) n/a 1872 6
1596.2.ew \(\chi_{1596}(143, \cdot)\) n/a 1872 6

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1596))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1596)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(399))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(532))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(798))\)\(^{\oplus 2}\)