## Defining parameters

 Level: $$N$$ = $$1150 = 2 \cdot 5^{2} \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Sturm bound: $$158400$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1150))$$.

Total New Old
Modular forms 40832 12118 28714
Cusp forms 38369 12118 26251
Eisenstein series 2463 0 2463

## Trace form

 $$12118 q + 2 q^{2} + 8 q^{3} + 2 q^{4} + 10 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} + 26 q^{9} + O(q^{10})$$ $$12118 q + 2 q^{2} + 8 q^{3} + 2 q^{4} + 10 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} + 26 q^{9} + 10 q^{10} + 24 q^{11} + 8 q^{12} + 28 q^{13} + 16 q^{14} + 40 q^{15} + 2 q^{16} + 18 q^{17} + 20 q^{18} - 18 q^{19} + 50 q^{21} - 34 q^{22} + 28 q^{23} - 32 q^{24} - 70 q^{25} + 10 q^{26} + 26 q^{27} - 2 q^{28} + 2 q^{29} - 40 q^{30} + 6 q^{31} - 8 q^{32} + 38 q^{33} - 14 q^{34} + 40 q^{35} + 26 q^{36} + 110 q^{37} + 40 q^{38} + 76 q^{39} + 10 q^{40} + 66 q^{41} + 64 q^{42} + 52 q^{43} + 24 q^{44} - 30 q^{45} + 24 q^{46} + 60 q^{47} + 8 q^{48} + 90 q^{49} + 50 q^{50} + 68 q^{51} + 28 q^{52} + 40 q^{53} + 102 q^{54} + 40 q^{55} + 38 q^{56} + 110 q^{57} + 104 q^{58} + 110 q^{59} + 92 q^{61} + 10 q^{62} + 38 q^{63} + 2 q^{64} - 70 q^{65} + 64 q^{66} + 20 q^{67} - 40 q^{68} + 66 q^{69} - 80 q^{70} + 94 q^{71} + 70 q^{72} + 32 q^{73} - 36 q^{74} - 120 q^{75} - 40 q^{76} - 18 q^{77} - 22 q^{78} + 110 q^{79} + 10 q^{80} + 214 q^{81} - 32 q^{82} - 64 q^{83} - 34 q^{84} - 30 q^{85} - 10 q^{86} + 26 q^{87} + 24 q^{88} - 8 q^{89} + 10 q^{90} + 108 q^{91} + 4 q^{92} + 136 q^{93} + 96 q^{94} + 32 q^{95} + 8 q^{96} - 284 q^{97} - 194 q^{98} - 512 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1150))$$

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
1150.2.a $$\chi_{1150}(1, \cdot)$$ 1150.2.a.a 1 1
1150.2.a.b 1
1150.2.a.c 1
1150.2.a.d 1
1150.2.a.e 1
1150.2.a.f 1
1150.2.a.g 1
1150.2.a.h 1
1150.2.a.i 1
1150.2.a.j 2
1150.2.a.k 2
1150.2.a.l 2
1150.2.a.m 2
1150.2.a.n 2
1150.2.a.o 2
1150.2.a.p 2
1150.2.a.q 3
1150.2.a.r 4
1150.2.a.s 4
1150.2.b $$\chi_{1150}(599, \cdot)$$ 1150.2.b.a 2 1
1150.2.b.b 2
1150.2.b.c 2
1150.2.b.d 2
1150.2.b.e 2
1150.2.b.f 4
1150.2.b.g 4
1150.2.b.h 4
1150.2.b.i 4
1150.2.b.j 6
1150.2.e $$\chi_{1150}(643, \cdot)$$ 1150.2.e.a 8 2
1150.2.e.b 8
1150.2.e.c 8
1150.2.e.d 16
1150.2.e.e 16
1150.2.e.f 16
1150.2.g $$\chi_{1150}(231, \cdot)$$ n/a 216 4
1150.2.i $$\chi_{1150}(139, \cdot)$$ n/a 224 4
1150.2.k $$\chi_{1150}(101, \cdot)$$ n/a 380 10
1150.2.m $$\chi_{1150}(137, \cdot)$$ n/a 480 8
1150.2.p $$\chi_{1150}(49, \cdot)$$ n/a 360 10
1150.2.r $$\chi_{1150}(7, \cdot)$$ n/a 720 20
1150.2.s $$\chi_{1150}(31, \cdot)$$ n/a 2400 40
1150.2.u $$\chi_{1150}(9, \cdot)$$ n/a 2400 40
1150.2.w $$\chi_{1150}(17, \cdot)$$ n/a 4800 80

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1150))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1150)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(230))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(575))$$$$^{\oplus 2}$$