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Properties

Label 2296.2
Level 2296
Weight 2
Dimension 86056
Nonzero newspaces 48
Sturm bound 645120
Trace bound 9

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Defining parameters

Level: \( N \) = \( 2296 = 2^{3} \cdot 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(645120\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2296))\).

Total New Old
Modular forms 164160 87616 76544
Cusp forms 158401 86056 72345
Eisenstein series 5759 1560 4199

Trace form

\( 86056 q - 148 q^{2} - 148 q^{3} - 148 q^{4} - 148 q^{6} - 188 q^{7} - 376 q^{8} - 284 q^{9} + O(q^{10}) \) \( 86056 q - 148 q^{2} - 148 q^{3} - 148 q^{4} - 148 q^{6} - 188 q^{7} - 376 q^{8} - 284 q^{9} - 148 q^{10} - 136 q^{11} - 148 q^{12} + 12 q^{13} - 188 q^{14} - 352 q^{15} - 148 q^{16} - 284 q^{17} - 184 q^{18} - 148 q^{19} - 184 q^{20} - 436 q^{22} - 184 q^{23} - 220 q^{24} - 332 q^{25} - 208 q^{26} - 208 q^{27} - 284 q^{28} - 244 q^{30} - 184 q^{31} - 208 q^{32} - 308 q^{33} - 220 q^{34} - 188 q^{35} - 436 q^{36} + 12 q^{37} - 184 q^{38} - 160 q^{39} - 208 q^{40} - 284 q^{41} - 316 q^{42} - 376 q^{43} - 100 q^{44} + 12 q^{45} - 88 q^{46} - 184 q^{47} - 28 q^{48} - 388 q^{49} - 292 q^{50} - 232 q^{51} - 40 q^{52} - 12 q^{53} - 4 q^{54} - 208 q^{55} - 104 q^{56} - 800 q^{57} - 88 q^{58} - 220 q^{59} - 16 q^{60} - 40 q^{62} - 260 q^{63} - 292 q^{64} - 276 q^{65} - 100 q^{66} - 64 q^{67} - 148 q^{68} + 136 q^{69} - 236 q^{70} - 288 q^{71} - 184 q^{72} - 100 q^{73} - 316 q^{74} + 52 q^{75} - 292 q^{76} + 44 q^{77} - 544 q^{78} - 24 q^{79} - 376 q^{80} - 4 q^{81} - 226 q^{82} - 220 q^{83} - 404 q^{84} + 340 q^{85} - 364 q^{86} - 72 q^{87} - 292 q^{88} - 148 q^{89} - 304 q^{90} - 4 q^{91} - 532 q^{92} + 148 q^{93} - 220 q^{94} + 24 q^{95} - 196 q^{96} - 232 q^{97} - 236 q^{98} - 112 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2296))\)

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
2296.2.a \(\chi_{2296}(1, \cdot)\) 2296.2.a.a 1 1
2296.2.a.b 1
2296.2.a.c 2
2296.2.a.d 3
2296.2.a.e 3
2296.2.a.f 4
2296.2.a.g 4
2296.2.a.h 4
2296.2.a.i 6
2296.2.a.j 7
2296.2.a.k 8
2296.2.a.l 8
2296.2.a.m 9
2296.2.b \(\chi_{2296}(1149, \cdot)\) n/a 240 1
2296.2.e \(\chi_{2296}(2295, \cdot)\) None 0 1
2296.2.f \(\chi_{2296}(1065, \cdot)\) 2296.2.f.a 2 1
2296.2.f.b 8
2296.2.f.c 22
2296.2.f.d 32
2296.2.i \(\chi_{2296}(83, \cdot)\) n/a 320 1
2296.2.j \(\chi_{2296}(1231, \cdot)\) None 0 1
2296.2.m \(\chi_{2296}(2213, \cdot)\) n/a 252 1
2296.2.n \(\chi_{2296}(1147, \cdot)\) n/a 332 1
2296.2.q \(\chi_{2296}(1313, \cdot)\) n/a 160 2
2296.2.s \(\chi_{2296}(419, \cdot)\) n/a 664 2
2296.2.u \(\chi_{2296}(337, \cdot)\) n/a 124 2
2296.2.w \(\chi_{2296}(1567, \cdot)\) None 0 2
2296.2.y \(\chi_{2296}(1485, \cdot)\) n/a 504 2
2296.2.z \(\chi_{2296}(57, \cdot)\) n/a 256 4
2296.2.bb \(\chi_{2296}(1475, \cdot)\) n/a 664 2
2296.2.be \(\chi_{2296}(1229, \cdot)\) n/a 664 2
2296.2.bf \(\chi_{2296}(1559, \cdot)\) None 0 2
2296.2.bi \(\chi_{2296}(411, \cdot)\) n/a 640 2
2296.2.bj \(\chi_{2296}(81, \cdot)\) n/a 168 2
2296.2.bm \(\chi_{2296}(327, \cdot)\) None 0 2
2296.2.bn \(\chi_{2296}(165, \cdot)\) n/a 640 2
2296.2.br \(\chi_{2296}(629, \cdot)\) n/a 1328 4
2296.2.bs \(\chi_{2296}(489, \cdot)\) n/a 336 4
2296.2.bv \(\chi_{2296}(547, \cdot)\) n/a 1008 4
2296.2.bw \(\chi_{2296}(407, \cdot)\) None 0 4
2296.2.bx \(\chi_{2296}(139, \cdot)\) n/a 1328 4
2296.2.ca \(\chi_{2296}(113, \cdot)\) n/a 256 4
2296.2.cb \(\chi_{2296}(783, \cdot)\) None 0 4
2296.2.ce \(\chi_{2296}(141, \cdot)\) n/a 1008 4
2296.2.ch \(\chi_{2296}(195, \cdot)\) n/a 1328 4
2296.2.ci \(\chi_{2296}(701, \cdot)\) n/a 1008 4
2296.2.cl \(\chi_{2296}(223, \cdot)\) None 0 4
2296.2.cm \(\chi_{2296}(501, \cdot)\) n/a 1328 4
2296.2.co \(\chi_{2296}(255, \cdot)\) None 0 4
2296.2.cq \(\chi_{2296}(9, \cdot)\) n/a 336 4
2296.2.cs \(\chi_{2296}(747, \cdot)\) n/a 1328 4
2296.2.cu \(\chi_{2296}(305, \cdot)\) n/a 672 8
2296.2.cv \(\chi_{2296}(197, \cdot)\) n/a 2016 8
2296.2.cx \(\chi_{2296}(279, \cdot)\) None 0 8
2296.2.cz \(\chi_{2296}(169, \cdot)\) n/a 496 8
2296.2.db \(\chi_{2296}(251, \cdot)\) n/a 2656 8
2296.2.dd \(\chi_{2296}(79, \cdot)\) None 0 8
2296.2.de \(\chi_{2296}(219, \cdot)\) n/a 2656 8
2296.2.dh \(\chi_{2296}(465, \cdot)\) n/a 672 8
2296.2.di \(\chi_{2296}(325, \cdot)\) n/a 2656 8
2296.2.dm \(\chi_{2296}(215, \cdot)\) None 0 8
2296.2.dn \(\chi_{2296}(277, \cdot)\) n/a 2656 8
2296.2.dq \(\chi_{2296}(187, \cdot)\) n/a 2656 8
2296.2.dt \(\chi_{2296}(37, \cdot)\) n/a 2656 8
2296.2.du \(\chi_{2296}(31, \cdot)\) None 0 8
2296.2.dx \(\chi_{2296}(25, \cdot)\) n/a 672 8
2296.2.dy \(\chi_{2296}(59, \cdot)\) n/a 2656 8
2296.2.ea \(\chi_{2296}(15, \cdot)\) None 0 16
2296.2.eb \(\chi_{2296}(99, \cdot)\) n/a 4032 16
2296.2.ee \(\chi_{2296}(97, \cdot)\) n/a 1344 16
2296.2.ef \(\chi_{2296}(13, \cdot)\) n/a 5312 16
2296.2.ej \(\chi_{2296}(115, \cdot)\) n/a 5312 16
2296.2.el \(\chi_{2296}(121, \cdot)\) n/a 1344 16
2296.2.en \(\chi_{2296}(87, \cdot)\) None 0 16
2296.2.ep \(\chi_{2296}(333, \cdot)\) n/a 5312 16
2296.2.es \(\chi_{2296}(101, \cdot)\) n/a 10624 32
2296.2.et \(\chi_{2296}(17, \cdot)\) n/a 2688 32
2296.2.ew \(\chi_{2296}(11, \cdot)\) n/a 10624 32
2296.2.ex \(\chi_{2296}(95, \cdot)\) None 0 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2296))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2296)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(287))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(328))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(574))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1148))\)\(^{\oplus 2}\)