## 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

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

## 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 the 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

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