## Defining parameters

 Level: $$N$$ = $$1143 = 3^{2} \cdot 127$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$32$$ Sturm bound: $$290304$$ Trace bound: $$6$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(1143))$$.

Total New Old
Modular forms 97776 77163 20613
Cusp forms 95760 76037 19723
Eisenstein series 2016 1126 890

## Trace form

 $$76037q - 183q^{2} - 246q^{3} - 187q^{4} - 201q^{5} - 270q^{6} - 185q^{7} - 189q^{8} - 234q^{9} + O(q^{10})$$ $$76037q - 183q^{2} - 246q^{3} - 187q^{4} - 201q^{5} - 270q^{6} - 185q^{7} - 189q^{8} - 234q^{9} - 543q^{10} - 183q^{11} - 264q^{12} - 197q^{13} - 201q^{14} - 252q^{15} - 211q^{16} - 189q^{17} - 252q^{18} - 611q^{19} - 177q^{20} - 240q^{21} - 195q^{22} - 93q^{23} - 162q^{24} - 163q^{25} - 189q^{26} - 360q^{27} - 575q^{28} - 345q^{29} - 288q^{30} - 125q^{31} - 243q^{32} - 270q^{33} - 135q^{34} - 189q^{35} - 234q^{36} - 431q^{37} - 123q^{38} - 204q^{39} - 249q^{40} - 147q^{41} - 252q^{42} - 311q^{43} - 189q^{44} - 144q^{45} - 759q^{46} - 21q^{47} - 318q^{48} - 279q^{49} - 267q^{50} - 414q^{51} - 197q^{52} - 189q^{53} - 90q^{54} - 543q^{55} - 129q^{56} - 186q^{57} - 33q^{58} - 363q^{59} - 288q^{60} - 77q^{61} - 189q^{62} - 324q^{63} - 283q^{64} - 237q^{65} - 216q^{66} - 251q^{67} - 135q^{68} - 252q^{69} - 213q^{70} - 189q^{71} - 522q^{72} - 827q^{73} - 393q^{74} - 174q^{75} - 167q^{76} - 201q^{77} - 324q^{78} - 113q^{79} - 189q^{80} - 90q^{81} - 651q^{82} - 21q^{83} - 240q^{84} - 81q^{85} + 177q^{86} + 216q^{87} - 219q^{88} - 189q^{89} - 360q^{90} - 535q^{91} - 285q^{92} - 636q^{93} - 357q^{94} - 321q^{95} - 252q^{96} - 419q^{97} - 189q^{98} - 252q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(1143))$$

We only show spaces with odd 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
1143.3.b $$\chi_{1143}(890, \cdot)$$ 1143.3.b.a 84 1
1143.3.d $$\chi_{1143}(253, \cdot)$$ n/a 105 1
1143.3.i $$\chi_{1143}(107, \cdot)$$ n/a 168 2
1143.3.k $$\chi_{1143}(616, \cdot)$$ n/a 508 2
1143.3.l $$\chi_{1143}(634, \cdot)$$ n/a 508 2
1143.3.m $$\chi_{1143}(274, \cdot)$$ n/a 508 2
1143.3.q $$\chi_{1143}(146, \cdot)$$ n/a 508 2
1143.3.r $$\chi_{1143}(128, \cdot)$$ n/a 504 2
1143.3.s $$\chi_{1143}(488, \cdot)$$ n/a 508 2
1143.3.t $$\chi_{1143}(235, \cdot)$$ n/a 210 2
1143.3.y $$\chi_{1143}(190, \cdot)$$ n/a 630 6
1143.3.ba $$\chi_{1143}(8, \cdot)$$ n/a 504 6
1143.3.bc $$\chi_{1143}(179, \cdot)$$ n/a 516 6
1143.3.bd $$\chi_{1143}(202, \cdot)$$ n/a 1524 6
1143.3.be $$\chi_{1143}(151, \cdot)$$ n/a 1524 6
1143.3.bf $$\chi_{1143}(164, \cdot)$$ n/a 1524 6
1143.3.bh $$\chi_{1143}(68, \cdot)$$ n/a 1524 6
1143.3.bj $$\chi_{1143}(28, \cdot)$$ n/a 636 6
1143.3.bo $$\chi_{1143}(10, \cdot)$$ n/a 1260 12
1143.3.bp $$\chi_{1143}(47, \cdot)$$ n/a 3048 12
1143.3.bq $$\chi_{1143}(2, \cdot)$$ n/a 3048 12
1143.3.br $$\chi_{1143}(38, \cdot)$$ n/a 3048 12
1143.3.bv $$\chi_{1143}(40, \cdot)$$ n/a 3048 12
1143.3.bw $$\chi_{1143}(238, \cdot)$$ n/a 3048 12
1143.3.bx $$\chi_{1143}(160, \cdot)$$ n/a 3048 12
1143.3.bz $$\chi_{1143}(152, \cdot)$$ n/a 1008 12
1143.3.cd $$\chi_{1143}(46, \cdot)$$ n/a 3816 36
1143.3.cf $$\chi_{1143}(41, \cdot)$$ n/a 9144 36
1143.3.ch $$\chi_{1143}(11, \cdot)$$ n/a 9144 36
1143.3.ci $$\chi_{1143}(7, \cdot)$$ n/a 9144 36
1143.3.cj $$\chi_{1143}(43, \cdot)$$ n/a 9144 36
1143.3.ck $$\chi_{1143}(17, \cdot)$$ n/a 3096 36

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

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(1143))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(1143)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(127))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(381))$$$$^{\oplus 2}$$