# Properties

 Label 1150.4 Level 1150 Weight 4 Dimension 36360 Nonzero newspaces 12 Sturm bound 316800 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$1150 = 2 \cdot 5^{2} \cdot 23$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$12$$ Sturm bound: $$316800$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1150))$$.

Total New Old
Modular forms 120032 36360 83672
Cusp forms 117568 36360 81208
Eisenstein series 2464 0 2464

## Trace form

 $$36360 q + 8 q^{2} - 32 q^{3} - 16 q^{4} - 10 q^{5} - 32 q^{6} - 16 q^{7} + 32 q^{8} + 332 q^{9} + O(q^{10})$$ $$36360 q + 8 q^{2} - 32 q^{3} - 16 q^{4} - 10 q^{5} - 32 q^{6} - 16 q^{7} + 32 q^{8} + 332 q^{9} + 100 q^{10} - 176 q^{11} - 128 q^{12} - 232 q^{13} - 448 q^{14} - 160 q^{15} + 192 q^{16} - 840 q^{17} - 692 q^{18} - 620 q^{19} + 160 q^{20} + 184 q^{21} + 1052 q^{22} + 176 q^{23} + 576 q^{24} + 2630 q^{25} + 388 q^{26} + 1708 q^{27} + 592 q^{28} - 320 q^{29} - 720 q^{30} - 756 q^{31} - 192 q^{32} - 2288 q^{33} - 1748 q^{34} - 2440 q^{35} - 144 q^{36} - 18 q^{37} - 800 q^{38} - 3348 q^{39} - 240 q^{40} - 1286 q^{41} + 256 q^{42} - 1028 q^{43} + 1088 q^{44} + 4550 q^{45} + 64 q^{46} + 732 q^{47} - 512 q^{48} - 1740 q^{49} - 700 q^{50} + 1844 q^{51} - 928 q^{52} + 4460 q^{53} + 4084 q^{54} + 2200 q^{55} + 3472 q^{56} + 10132 q^{57} + 1128 q^{58} - 3130 q^{59} - 5440 q^{60} - 5072 q^{61} - 10340 q^{62} - 27012 q^{63} - 256 q^{64} - 6170 q^{65} - 6880 q^{66} - 4120 q^{67} + 1904 q^{68} - 2968 q^{69} + 9600 q^{70} - 4196 q^{71} - 1280 q^{72} + 10856 q^{73} + 7408 q^{74} + 24080 q^{75} + 2240 q^{76} + 22008 q^{77} + 17564 q^{78} + 18886 q^{79} - 160 q^{80} + 15632 q^{81} + 4392 q^{82} + 2882 q^{83} + 712 q^{84} - 13210 q^{85} + 4324 q^{86} - 22766 q^{87} + 384 q^{88} - 22020 q^{89} - 17340 q^{90} - 14260 q^{91} - 3584 q^{92} - 11024 q^{93} - 5248 q^{94} - 19288 q^{95} - 512 q^{96} - 81902 q^{97} - 51280 q^{98} - 90826 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1150))$$

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
1150.4.a $$\chi_{1150}(1, \cdot)$$ 1150.4.a.a 1 1
1150.4.a.b 1
1150.4.a.c 1
1150.4.a.d 1
1150.4.a.e 1
1150.4.a.f 1
1150.4.a.g 1
1150.4.a.h 1
1150.4.a.i 1
1150.4.a.j 2
1150.4.a.k 2
1150.4.a.l 2
1150.4.a.m 3
1150.4.a.n 4
1150.4.a.o 4
1150.4.a.p 4
1150.4.a.q 5
1150.4.a.r 5
1150.4.a.s 5
1150.4.a.t 5
1150.4.a.u 5
1150.4.a.v 5
1150.4.a.w 6
1150.4.a.x 6
1150.4.a.y 7
1150.4.a.z 7
1150.4.a.ba 9
1150.4.a.bb 9
1150.4.b $$\chi_{1150}(599, \cdot)$$ 1150.4.b.a 2 1
1150.4.b.b 2
1150.4.b.c 2
1150.4.b.d 2
1150.4.b.e 2
1150.4.b.f 2
1150.4.b.g 2
1150.4.b.h 2
1150.4.b.i 4
1150.4.b.j 4
1150.4.b.k 4
1150.4.b.l 6
1150.4.b.m 8
1150.4.b.n 8
1150.4.b.o 8
1150.4.b.p 10
1150.4.b.q 10
1150.4.b.r 10
1150.4.b.s 12
1150.4.e $$\chi_{1150}(643, \cdot)$$ n/a 216 2
1150.4.g $$\chi_{1150}(231, \cdot)$$ n/a 664 4
1150.4.i $$\chi_{1150}(139, \cdot)$$ n/a 656 4
1150.4.k $$\chi_{1150}(101, \cdot)$$ n/a 1140 10
1150.4.m $$\chi_{1150}(137, \cdot)$$ n/a 1440 8
1150.4.p $$\chi_{1150}(49, \cdot)$$ n/a 1080 10
1150.4.r $$\chi_{1150}(7, \cdot)$$ n/a 2160 20
1150.4.s $$\chi_{1150}(31, \cdot)$$ n/a 7200 40
1150.4.u $$\chi_{1150}(9, \cdot)$$ n/a 7200 40
1150.4.w $$\chi_{1150}(17, \cdot)$$ n/a 14400 80

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1150))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(1150)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(230))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(575))$$$$^{\oplus 2}$$