## Defining parameters

 Level: $$N$$ = $$1148 = 2^{2} \cdot 7 \cdot 41$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$161280$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1148))$$.

Total New Old
Modular forms 41520 22900 18620
Cusp forms 39121 22124 16997
Eisenstein series 2399 776 1623

## Trace form

 $$22124 q - 74 q^{2} + 2 q^{3} - 74 q^{4} - 142 q^{5} - 80 q^{6} + 8 q^{7} - 194 q^{8} - 152 q^{9} + O(q^{10})$$ $$22124 q - 74 q^{2} + 2 q^{3} - 74 q^{4} - 142 q^{5} - 80 q^{6} + 8 q^{7} - 194 q^{8} - 152 q^{9} - 92 q^{10} - 6 q^{11} - 104 q^{12} - 168 q^{13} - 118 q^{14} - 12 q^{15} - 98 q^{16} - 142 q^{17} - 86 q^{18} - 2 q^{19} - 80 q^{20} - 210 q^{21} - 164 q^{22} + 6 q^{23} - 56 q^{24} - 164 q^{25} - 56 q^{26} + 20 q^{27} - 46 q^{28} - 400 q^{29} - 68 q^{30} + 26 q^{31} - 74 q^{32} - 58 q^{33} - 80 q^{34} + 10 q^{35} - 218 q^{36} - 54 q^{37} - 116 q^{38} + 164 q^{39} - 144 q^{40} - 132 q^{41} - 224 q^{42} + 56 q^{43} - 116 q^{44} - 12 q^{45} - 104 q^{46} + 102 q^{47} - 80 q^{48} - 128 q^{49} - 206 q^{50} + 126 q^{51} - 80 q^{52} - 78 q^{53} - 44 q^{54} + 36 q^{55} - 118 q^{56} - 324 q^{57} - 68 q^{58} + 18 q^{59} - 56 q^{60} - 126 q^{61} - 80 q^{62} + 20 q^{63} - 218 q^{64} - 192 q^{65} - 228 q^{66} - 134 q^{67} - 280 q^{68} - 332 q^{69} - 312 q^{70} - 160 q^{71} - 410 q^{72} - 382 q^{73} - 296 q^{74} - 312 q^{75} - 680 q^{76} - 322 q^{77} - 648 q^{78} - 186 q^{79} - 432 q^{80} - 650 q^{81} - 572 q^{82} - 208 q^{83} - 340 q^{84} - 800 q^{85} - 444 q^{86} - 172 q^{87} - 516 q^{88} - 398 q^{89} - 680 q^{90} - 144 q^{91} - 428 q^{92} - 346 q^{93} - 380 q^{94} - 166 q^{95} - 432 q^{96} - 280 q^{97} - 170 q^{98} - 144 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1148))$$

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
1148.2.a $$\chi_{1148}(1, \cdot)$$ 1148.2.a.a 2 1
1148.2.a.b 3
1148.2.a.c 5
1148.2.a.d 5
1148.2.a.e 5
1148.2.c $$\chi_{1148}(1147, \cdot)$$ n/a 164 1
1148.2.d $$\chi_{1148}(1065, \cdot)$$ 1148.2.d.a 20 1
1148.2.f $$\chi_{1148}(83, \cdot)$$ n/a 160 1
1148.2.i $$\chi_{1148}(165, \cdot)$$ 1148.2.i.a 2 2
1148.2.i.b 2
1148.2.i.c 2
1148.2.i.d 16
1148.2.i.e 30
1148.2.k $$\chi_{1148}(337, \cdot)$$ 1148.2.k.a 8 2
1148.2.k.b 36
1148.2.l $$\chi_{1148}(419, \cdot)$$ n/a 328 2
1148.2.n $$\chi_{1148}(57, \cdot)$$ 1148.2.n.a 8 4
1148.2.n.b 8
1148.2.n.c 16
1148.2.n.d 24
1148.2.n.e 24
1148.2.p $$\chi_{1148}(411, \cdot)$$ n/a 320 2
1148.2.r $$\chi_{1148}(81, \cdot)$$ 1148.2.r.a 56 2
1148.2.u $$\chi_{1148}(327, \cdot)$$ n/a 328 2
1148.2.w $$\chi_{1148}(489, \cdot)$$ n/a 112 4
1148.2.y $$\chi_{1148}(407, \cdot)$$ n/a 504 4
1148.2.ba $$\chi_{1148}(113, \cdot)$$ 1148.2.ba.a 80 4
1148.2.bb $$\chi_{1148}(195, \cdot)$$ n/a 656 4
1148.2.bf $$\chi_{1148}(139, \cdot)$$ n/a 656 4
1148.2.bh $$\chi_{1148}(255, \cdot)$$ n/a 656 4
1148.2.bi $$\chi_{1148}(9, \cdot)$$ n/a 112 4
1148.2.bk $$\chi_{1148}(37, \cdot)$$ n/a 224 8
1148.2.bm $$\chi_{1148}(251, \cdot)$$ n/a 1312 8
1148.2.bn $$\chi_{1148}(169, \cdot)$$ n/a 176 8
1148.2.bp $$\chi_{1148}(79, \cdot)$$ n/a 1312 8
1148.2.br $$\chi_{1148}(325, \cdot)$$ n/a 224 8
1148.2.bu $$\chi_{1148}(59, \cdot)$$ n/a 1312 8
1148.2.bw $$\chi_{1148}(31, \cdot)$$ n/a 1312 8
1148.2.bz $$\chi_{1148}(25, \cdot)$$ n/a 224 8
1148.2.ca $$\chi_{1148}(15, \cdot)$$ n/a 2016 16
1148.2.cc $$\chi_{1148}(13, \cdot)$$ n/a 448 16
1148.2.cf $$\chi_{1148}(121, \cdot)$$ n/a 448 16
1148.2.cg $$\chi_{1148}(87, \cdot)$$ n/a 2624 16
1148.2.cj $$\chi_{1148}(17, \cdot)$$ n/a 896 32
1148.2.cl $$\chi_{1148}(11, \cdot)$$ n/a 5248 32

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1148))$$ into lower level spaces

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