# Properties

 Label 1175.4 Level 1175 Weight 4 Dimension 151567 Nonzero newspaces 12 Sturm bound 441600 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$1175 = 5^{2} \cdot 47$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$12$$ Sturm bound: $$441600$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1175))$$.

Total New Old
Modular forms 166888 153411 13477
Cusp forms 164312 151567 12745
Eisenstein series 2576 1844 732

## Trace form

 $$151567q - 295q^{2} - 271q^{3} - 247q^{4} - 358q^{5} - 479q^{6} - 255q^{7} - 279q^{8} - 371q^{9} + O(q^{10})$$ $$151567q - 295q^{2} - 271q^{3} - 247q^{4} - 358q^{5} - 479q^{6} - 255q^{7} - 279q^{8} - 371q^{9} - 308q^{10} - 319q^{11} - 215q^{12} - 431q^{13} - 375q^{14} - 368q^{15} - 191q^{16} + 465q^{17} + 989q^{18} + 361q^{19} - 708q^{20} - 879q^{21} - 2231q^{22} - 1471q^{23} - 3139q^{24} - 1738q^{25} - 1159q^{26} - 1759q^{27} - 1527q^{28} - 639q^{29} + 212q^{30} - 159q^{31} + 2985q^{32} + 1897q^{33} + 2605q^{34} + 1312q^{35} - 4319q^{36} + 843q^{37} + 1905q^{38} + 3607q^{39} + 3752q^{40} + 1665q^{41} + 4517q^{42} + 1711q^{43} + 1765q^{44} - 4758q^{45} + 570q^{46} - 921q^{47} - 3030q^{48} - 4057q^{49} - 9368q^{50} - 3329q^{51} - 7603q^{52} - 3509q^{53} - 7599q^{54} - 2188q^{55} - 6335q^{56} - 2775q^{57} - 215q^{58} + 5791q^{59} + 22572q^{60} + 1349q^{61} + 21989q^{62} + 15609q^{63} + 13093q^{64} + 3542q^{65} + 1745q^{66} - 1215q^{67} - 7127q^{68} - 7063q^{69} - 8748q^{70} - 3759q^{71} - 18779q^{72} - 9551q^{73} - 19315q^{74} - 12088q^{75} - 17981q^{76} - 18625q^{77} - 31209q^{78} - 12963q^{79} - 12028q^{80} - 4185q^{81} + 4976q^{82} + 13627q^{83} + 27333q^{84} + 18922q^{85} + 16209q^{86} + 21333q^{87} + 42309q^{88} + 21087q^{89} + 15952q^{90} + 22251q^{91} + 25838q^{92} - 930q^{93} + 18451q^{94} - 14356q^{95} + 13789q^{96} - 17323q^{97} - 7256q^{98} - 12473q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1175))$$

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
1175.4.a $$\chi_{1175}(1, \cdot)$$ 1175.4.a.a 3 1
1175.4.a.b 8
1175.4.a.c 8
1175.4.a.d 10
1175.4.a.e 13
1175.4.a.f 15
1175.4.a.g 18
1175.4.a.h 18
1175.4.a.i 28
1175.4.a.j 28
1175.4.a.k 35
1175.4.a.l 35
1175.4.c $$\chi_{1175}(424, \cdot)$$ n/a 206 1
1175.4.e $$\chi_{1175}(93, \cdot)$$ n/a 428 2
1175.4.g $$\chi_{1175}(236, \cdot)$$ n/a 1376 4
1175.4.i $$\chi_{1175}(189, \cdot)$$ n/a 1384 4
1175.4.l $$\chi_{1175}(187, \cdot)$$ n/a 2864 8
1175.4.m $$\chi_{1175}(51, \cdot)$$ n/a 4950 22
1175.4.o $$\chi_{1175}(24, \cdot)$$ n/a 4708 22
1175.4.r $$\chi_{1175}(43, \cdot)$$ n/a 9416 44
1175.4.s $$\chi_{1175}(6, \cdot)$$ n/a 31504 88
1175.4.u $$\chi_{1175}(4, \cdot)$$ n/a 31504 88
1175.4.w $$\chi_{1175}(13, \cdot)$$ n/a 63008 176

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1175))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(1175)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(47))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(235))$$$$^{\oplus 2}$$