# Properties

 Label 475.3 Level 475 Weight 3 Dimension 16149 Nonzero newspaces 18 Sturm bound 54000 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$475 = 5^{2} \cdot 19$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$18$$ Sturm bound: $$54000$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(475))$$.

Total New Old
Modular forms 18504 16847 1657
Cusp forms 17496 16149 1347
Eisenstein series 1008 698 310

## Trace form

 $$16149q - 97q^{2} - 97q^{3} - 97q^{4} - 124q^{5} - 153q^{6} - 97q^{7} - 97q^{8} - 97q^{9} + O(q^{10})$$ $$16149q - 97q^{2} - 97q^{3} - 97q^{4} - 124q^{5} - 153q^{6} - 97q^{7} - 97q^{8} - 97q^{9} - 124q^{10} - 153q^{11} - 25q^{12} - 37q^{13} - 25q^{14} - 124q^{15} - 209q^{16} - 228q^{17} - 388q^{18} - 228q^{19} - 548q^{20} - 336q^{21} - 365q^{22} - 182q^{23} - 333q^{24} - 64q^{25} - 377q^{26} + 65q^{27} + 506q^{28} + 247q^{29} + 356q^{30} + 235q^{31} + 688q^{32} + 479q^{33} + 538q^{34} + 96q^{35} + 5q^{36} - 208q^{37} - 500q^{38} - 1122q^{39} - 1024q^{40} - 545q^{41} - 1947q^{42} - 754q^{43} - 788q^{44} - 764q^{45} - 558q^{46} - 194q^{47} - 626q^{48} - 186q^{49} + 56q^{50} + 26q^{51} + 787q^{52} + 371q^{53} + 1392q^{54} + 356q^{55} + 440q^{56} + 488q^{57} + 974q^{58} + 268q^{59} + 956q^{60} + 47q^{61} + 24q^{62} + 247q^{63} - 533q^{64} - 864q^{65} - 609q^{66} - 312q^{67} - 1852q^{68} - 716q^{69} - 764q^{70} - 654q^{71} - 1872q^{72} - 66q^{73} - 9q^{74} + 36q^{75} - 399q^{76} - 985q^{77} - 3455q^{78} - 1923q^{79} - 1468q^{80} - 4003q^{81} - 4146q^{82} - 2484q^{83} - 8629q^{84} - 2640q^{85} - 2982q^{86} - 5109q^{87} - 5213q^{88} - 1798q^{89} - 2344q^{90} - 2277q^{91} - 1830q^{92} - 2201q^{93} - 1760q^{94} - 346q^{95} + 2298q^{96} + 486q^{97} + 3044q^{98} + 3285q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(475))$$

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
475.3.c $$\chi_{475}(151, \cdot)$$ 475.3.c.a 1 1
475.3.c.b 2
475.3.c.c 2
475.3.c.d 4
475.3.c.e 4
475.3.c.f 8
475.3.c.g 12
475.3.c.h 14
475.3.c.i 14
475.3.d $$\chi_{475}(474, \cdot)$$ 475.3.d.a 2 1
475.3.d.b 4
475.3.d.c 24
475.3.d.d 28
475.3.f $$\chi_{475}(343, \cdot)$$ n/a 108 2
475.3.i $$\chi_{475}(274, \cdot)$$ n/a 116 2
475.3.k $$\chi_{475}(126, \cdot)$$ n/a 122 2
475.3.m $$\chi_{475}(94, \cdot)$$ n/a 392 4
475.3.o $$\chi_{475}(56, \cdot)$$ n/a 392 4
475.3.q $$\chi_{475}(7, \cdot)$$ n/a 232 4
475.3.s $$\chi_{475}(51, \cdot)$$ n/a 360 6
475.3.t $$\chi_{475}(124, \cdot)$$ n/a 348 6
475.3.w $$\chi_{475}(58, \cdot)$$ n/a 720 8
475.3.y $$\chi_{475}(31, \cdot)$$ n/a 784 8
475.3.z $$\chi_{475}(69, \cdot)$$ n/a 784 8
475.3.ba $$\chi_{475}(43, \cdot)$$ n/a 696 12
475.3.bd $$\chi_{475}(83, \cdot)$$ n/a 1568 16
475.3.bf $$\chi_{475}(21, \cdot)$$ n/a 2352 24
475.3.bh $$\chi_{475}(14, \cdot)$$ n/a 2352 24
475.3.bj $$\chi_{475}(17, \cdot)$$ n/a 4704 48

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

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(475))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(475)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 2}$$