Properties

Label 2496.2
Level 2496
Weight 2
Dimension 71228
Nonzero newspaces 56
Sturm bound 688128
Trace bound 43

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Defining parameters

Level: \( N \) = \( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(688128\)
Trace bound: \(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2496))\).

Total New Old
Modular forms 175488 72196 103292
Cusp forms 168577 71228 97349
Eisenstein series 6911 968 5943

Trace form

\( 71228q - 60q^{3} - 160q^{4} - 80q^{6} - 128q^{7} - 100q^{9} + O(q^{10}) \) \( 71228q - 60q^{3} - 160q^{4} - 80q^{6} - 128q^{7} - 100q^{9} - 160q^{10} - 16q^{11} - 80q^{12} - 192q^{13} - 72q^{15} - 160q^{16} - 32q^{17} - 80q^{18} - 152q^{19} - 72q^{21} - 128q^{22} - 156q^{25} + 80q^{26} - 108q^{27} + 64q^{29} + 80q^{30} - 32q^{31} + 160q^{32} + 16q^{33} + 48q^{35} + 80q^{36} - 96q^{37} + 160q^{38} - 44q^{39} - 192q^{40} + 64q^{41} - 104q^{43} + 32q^{44} + 8q^{45} - 160q^{46} - 80q^{48} - 252q^{49} - 96q^{50} + 72q^{51} - 272q^{52} - 112q^{54} + 192q^{55} - 224q^{56} - 48q^{57} - 448q^{58} + 320q^{59} - 272q^{60} - 160q^{61} - 192q^{62} + 8q^{63} - 544q^{64} + 16q^{65} - 336q^{66} + 232q^{67} - 192q^{68} - 152q^{69} - 544q^{70} + 256q^{71} - 80q^{72} - 200q^{73} - 224q^{74} + 36q^{75} - 416q^{76} - 96q^{77} - 160q^{78} - 176q^{79} - 96q^{80} - 268q^{81} - 160q^{82} - 80q^{83} - 304q^{84} - 256q^{85} - 176q^{87} - 160q^{88} - 64q^{89} - 368q^{90} - 192q^{91} - 192q^{93} - 160q^{94} - 96q^{95} - 352q^{96} - 216q^{97} - 176q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2496))\)

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
2496.2.a \(\chi_{2496}(1, \cdot)\) 2496.2.a.a 1 1
2496.2.a.b 1
2496.2.a.c 1
2496.2.a.d 1
2496.2.a.e 1
2496.2.a.f 1
2496.2.a.g 1
2496.2.a.h 1
2496.2.a.i 1
2496.2.a.j 1
2496.2.a.k 1
2496.2.a.l 1
2496.2.a.m 1
2496.2.a.n 1
2496.2.a.o 1
2496.2.a.p 1
2496.2.a.q 1
2496.2.a.r 1
2496.2.a.s 1
2496.2.a.t 1
2496.2.a.u 1
2496.2.a.v 1
2496.2.a.w 1
2496.2.a.x 1
2496.2.a.y 1
2496.2.a.z 1
2496.2.a.ba 1
2496.2.a.bb 1
2496.2.a.bc 1
2496.2.a.bd 1
2496.2.a.be 2
2496.2.a.bf 2
2496.2.a.bg 2
2496.2.a.bh 2
2496.2.a.bi 2
2496.2.a.bj 2
2496.2.a.bk 3
2496.2.a.bl 3
2496.2.c \(\chi_{2496}(961, \cdot)\) 2496.2.c.a 2 1
2496.2.c.b 2
2496.2.c.c 2
2496.2.c.d 2
2496.2.c.e 2
2496.2.c.f 2
2496.2.c.g 2
2496.2.c.h 2
2496.2.c.i 2
2496.2.c.j 2
2496.2.c.k 2
2496.2.c.l 2
2496.2.c.m 2
2496.2.c.n 2
2496.2.c.o 6
2496.2.c.p 6
2496.2.c.q 8
2496.2.c.r 8
2496.2.d \(\chi_{2496}(1535, \cdot)\) 2496.2.d.a 2 1
2496.2.d.b 2
2496.2.d.c 2
2496.2.d.d 2
2496.2.d.e 2
2496.2.d.f 2
2496.2.d.g 2
2496.2.d.h 2
2496.2.d.i 4
2496.2.d.j 4
2496.2.d.k 4
2496.2.d.l 4
2496.2.d.m 8
2496.2.d.n 8
2496.2.d.o 12
2496.2.d.p 16
2496.2.d.q 20
2496.2.g \(\chi_{2496}(1249, \cdot)\) 2496.2.g.a 4 1
2496.2.g.b 4
2496.2.g.c 4
2496.2.g.d 4
2496.2.g.e 8
2496.2.g.f 8
2496.2.g.g 8
2496.2.g.h 8
2496.2.h \(\chi_{2496}(1247, \cdot)\) n/a 112 1
2496.2.j \(\chi_{2496}(287, \cdot)\) 2496.2.j.a 4 1
2496.2.j.b 4
2496.2.j.c 12
2496.2.j.d 12
2496.2.j.e 32
2496.2.j.f 32
2496.2.m \(\chi_{2496}(2209, \cdot)\) 2496.2.m.a 8 1
2496.2.m.b 8
2496.2.m.c 16
2496.2.m.d 24
2496.2.n \(\chi_{2496}(2495, \cdot)\) n/a 108 1
2496.2.q \(\chi_{2496}(1153, \cdot)\) n/a 112 2
2496.2.r \(\chi_{2496}(463, \cdot)\) n/a 112 2
2496.2.u \(\chi_{2496}(593, \cdot)\) n/a 216 2
2496.2.v \(\chi_{2496}(623, \cdot)\) n/a 216 2
2496.2.x \(\chi_{2496}(625, \cdot)\) 2496.2.x.a 40 2
2496.2.x.b 56
2496.2.bb \(\chi_{2496}(31, \cdot)\) n/a 112 2
2496.2.bc \(\chi_{2496}(1087, \cdot)\) n/a 112 2
2496.2.bf \(\chi_{2496}(1217, \cdot)\) n/a 216 2
2496.2.bg \(\chi_{2496}(161, \cdot)\) n/a 224 2
2496.2.bh \(\chi_{2496}(911, \cdot)\) n/a 192 2
2496.2.bj \(\chi_{2496}(337, \cdot)\) n/a 112 2
2496.2.bm \(\chi_{2496}(785, \cdot)\) n/a 216 2
2496.2.bn \(\chi_{2496}(655, \cdot)\) n/a 112 2
2496.2.bq \(\chi_{2496}(95, \cdot)\) n/a 224 2
2496.2.br \(\chi_{2496}(289, \cdot)\) n/a 112 2
2496.2.bu \(\chi_{2496}(191, \cdot)\) n/a 216 2
2496.2.bv \(\chi_{2496}(1921, \cdot)\) n/a 112 2
2496.2.bz \(\chi_{2496}(959, \cdot)\) n/a 216 2
2496.2.ca \(\chi_{2496}(673, \cdot)\) n/a 112 2
2496.2.cd \(\chi_{2496}(1439, \cdot)\) n/a 224 2
2496.2.cf \(\chi_{2496}(473, \cdot)\) None 0 4
2496.2.ch \(\chi_{2496}(343, \cdot)\) None 0 4
2496.2.ci \(\chi_{2496}(25, \cdot)\) None 0 4
2496.2.ck \(\chi_{2496}(313, \cdot)\) None 0 4
2496.2.cn \(\chi_{2496}(599, \cdot)\) None 0 4
2496.2.cp \(\chi_{2496}(311, \cdot)\) None 0 4
2496.2.cq \(\chi_{2496}(281, \cdot)\) None 0 4
2496.2.cs \(\chi_{2496}(151, \cdot)\) None 0 4
2496.2.cu \(\chi_{2496}(305, \cdot)\) n/a 432 4
2496.2.cx \(\chi_{2496}(175, \cdot)\) n/a 224 4
2496.2.cz \(\chi_{2496}(49, \cdot)\) n/a 224 4
2496.2.db \(\chi_{2496}(815, \cdot)\) n/a 432 4
2496.2.dc \(\chi_{2496}(353, \cdot)\) n/a 448 4
2496.2.dd \(\chi_{2496}(449, \cdot)\) n/a 432 4
2496.2.dg \(\chi_{2496}(319, \cdot)\) n/a 224 4
2496.2.dh \(\chi_{2496}(223, \cdot)\) n/a 224 4
2496.2.dl \(\chi_{2496}(529, \cdot)\) n/a 224 4
2496.2.dn \(\chi_{2496}(335, \cdot)\) n/a 432 4
2496.2.dp \(\chi_{2496}(847, \cdot)\) n/a 224 4
2496.2.dq \(\chi_{2496}(977, \cdot)\) n/a 432 4
2496.2.ds \(\chi_{2496}(157, \cdot)\) n/a 1536 8
2496.2.dt \(\chi_{2496}(155, \cdot)\) n/a 3552 8
2496.2.dw \(\chi_{2496}(5, \cdot)\) n/a 3552 8
2496.2.dx \(\chi_{2496}(187, \cdot)\) n/a 1792 8
2496.2.ea \(\chi_{2496}(317, \cdot)\) n/a 3552 8
2496.2.eb \(\chi_{2496}(499, \cdot)\) n/a 1792 8
2496.2.ee \(\chi_{2496}(131, \cdot)\) n/a 3072 8
2496.2.ef \(\chi_{2496}(181, \cdot)\) n/a 1792 8
2496.2.ej \(\chi_{2496}(487, \cdot)\) None 0 8
2496.2.el \(\chi_{2496}(41, \cdot)\) None 0 8
2496.2.en \(\chi_{2496}(263, \cdot)\) None 0 8
2496.2.ep \(\chi_{2496}(23, \cdot)\) None 0 8
2496.2.eq \(\chi_{2496}(121, \cdot)\) None 0 8
2496.2.es \(\chi_{2496}(217, \cdot)\) None 0 8
2496.2.eu \(\chi_{2496}(7, \cdot)\) None 0 8
2496.2.ew \(\chi_{2496}(137, \cdot)\) None 0 8
2496.2.fa \(\chi_{2496}(179, \cdot)\) n/a 7104 16
2496.2.fb \(\chi_{2496}(61, \cdot)\) n/a 3584 16
2496.2.fe \(\chi_{2496}(115, \cdot)\) n/a 3584 16
2496.2.ff \(\chi_{2496}(149, \cdot)\) n/a 7104 16
2496.2.fi \(\chi_{2496}(19, \cdot)\) n/a 3584 16
2496.2.fj \(\chi_{2496}(245, \cdot)\) n/a 7104 16
2496.2.fm \(\chi_{2496}(205, \cdot)\) n/a 3584 16
2496.2.fn \(\chi_{2496}(35, \cdot)\) n/a 7104 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2496))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2496)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(624))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(832))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1248))\)\(^{\oplus 2}\)