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Properties

Label 1288.2
Level 1288
Weight 2
Dimension 26800
Nonzero newspaces 24
Sturm bound 202752
Trace bound 8

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Defining parameters

Level: \( N \) = \( 1288 = 2^{3} \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(202752\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1288))\).

Total New Old
Modular forms 52272 27640 24632
Cusp forms 49105 26800 22305
Eisenstein series 3167 840 2327

Trace form

\( 26800 q - 76 q^{2} - 76 q^{3} - 76 q^{4} - 76 q^{6} - 98 q^{7} - 196 q^{8} - 140 q^{9} + O(q^{10}) \) \( 26800 q - 76 q^{2} - 76 q^{3} - 76 q^{4} - 76 q^{6} - 98 q^{7} - 196 q^{8} - 140 q^{9} - 76 q^{10} - 64 q^{11} - 76 q^{12} + 12 q^{13} - 98 q^{14} - 172 q^{15} - 76 q^{16} - 140 q^{17} - 112 q^{18} - 76 q^{19} - 112 q^{20} - 256 q^{22} - 100 q^{23} - 236 q^{24} - 188 q^{25} - 136 q^{26} - 136 q^{27} - 194 q^{28} - 172 q^{30} - 112 q^{31} - 136 q^{32} - 164 q^{33} - 148 q^{34} - 76 q^{35} - 256 q^{36} + 100 q^{37} - 112 q^{38} - 136 q^{40} - 60 q^{41} - 26 q^{42} - 108 q^{43} - 28 q^{44} + 144 q^{45} - 52 q^{46} - 112 q^{47} + 44 q^{48} - 142 q^{49} - 112 q^{50} - 72 q^{51} + 32 q^{52} + 32 q^{53} + 68 q^{54} - 48 q^{55} - 14 q^{56} - 352 q^{57} - 16 q^{58} - 104 q^{59} + 56 q^{60} + 32 q^{62} - 170 q^{63} - 112 q^{64} - 152 q^{65} - 160 q^{66} - 112 q^{67} - 76 q^{68} - 12 q^{69} - 256 q^{70} - 268 q^{71} - 112 q^{72} - 116 q^{73} - 288 q^{74} - 328 q^{75} - 440 q^{76} - 36 q^{77} - 804 q^{78} - 244 q^{79} - 700 q^{80} - 464 q^{81} - 484 q^{82} - 280 q^{83} - 622 q^{84} - 132 q^{85} - 732 q^{86} - 556 q^{87} - 572 q^{88} - 296 q^{89} - 1068 q^{90} - 228 q^{91} - 682 q^{92} - 12 q^{93} - 544 q^{94} - 328 q^{95} - 960 q^{96} - 380 q^{97} - 168 q^{98} - 448 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1288))\)

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
1288.2.a \(\chi_{1288}(1, \cdot)\) 1288.2.a.a 1 1
1288.2.a.b 1
1288.2.a.c 1
1288.2.a.d 1
1288.2.a.e 1
1288.2.a.f 1
1288.2.a.g 1
1288.2.a.h 1
1288.2.a.i 1
1288.2.a.j 2
1288.2.a.k 2
1288.2.a.l 3
1288.2.a.m 3
1288.2.a.n 4
1288.2.a.o 4
1288.2.a.p 5
1288.2.b \(\chi_{1288}(645, \cdot)\) n/a 132 1
1288.2.e \(\chi_{1288}(183, \cdot)\) None 0 1
1288.2.f \(\chi_{1288}(321, \cdot)\) 1288.2.f.a 24 1
1288.2.f.b 24
1288.2.i \(\chi_{1288}(139, \cdot)\) n/a 176 1
1288.2.j \(\chi_{1288}(783, \cdot)\) None 0 1
1288.2.m \(\chi_{1288}(965, \cdot)\) n/a 188 1
1288.2.n \(\chi_{1288}(827, \cdot)\) n/a 144 1
1288.2.q \(\chi_{1288}(737, \cdot)\) 1288.2.q.a 22 2
1288.2.q.b 22
1288.2.q.c 22
1288.2.q.d 22
1288.2.s \(\chi_{1288}(275, \cdot)\) n/a 376 2
1288.2.v \(\chi_{1288}(45, \cdot)\) n/a 376 2
1288.2.w \(\chi_{1288}(47, \cdot)\) None 0 2
1288.2.z \(\chi_{1288}(507, \cdot)\) n/a 352 2
1288.2.ba \(\chi_{1288}(689, \cdot)\) 1288.2.ba.a 48 2
1288.2.ba.b 48
1288.2.bd \(\chi_{1288}(919, \cdot)\) None 0 2
1288.2.be \(\chi_{1288}(93, \cdot)\) n/a 352 2
1288.2.bg \(\chi_{1288}(169, \cdot)\) n/a 360 10
1288.2.bj \(\chi_{1288}(43, \cdot)\) n/a 1440 10
1288.2.bk \(\chi_{1288}(125, \cdot)\) n/a 1880 10
1288.2.bn \(\chi_{1288}(55, \cdot)\) None 0 10
1288.2.bo \(\chi_{1288}(27, \cdot)\) n/a 1880 10
1288.2.br \(\chi_{1288}(97, \cdot)\) n/a 480 10
1288.2.bs \(\chi_{1288}(15, \cdot)\) None 0 10
1288.2.bv \(\chi_{1288}(29, \cdot)\) n/a 1440 10
1288.2.bw \(\chi_{1288}(9, \cdot)\) n/a 960 20
1288.2.by \(\chi_{1288}(165, \cdot)\) n/a 3760 20
1288.2.bz \(\chi_{1288}(79, \cdot)\) None 0 20
1288.2.cc \(\chi_{1288}(17, \cdot)\) n/a 960 20
1288.2.cd \(\chi_{1288}(3, \cdot)\) n/a 3760 20
1288.2.cg \(\chi_{1288}(31, \cdot)\) None 0 20
1288.2.ch \(\chi_{1288}(5, \cdot)\) n/a 3760 20
1288.2.ck \(\chi_{1288}(11, \cdot)\) n/a 3760 20

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1288))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1288)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(644))\)\(^{\oplus 2}\)