# Properties

 Label 525.4 Level 525 Weight 4 Dimension 18874 Nonzero newspaces 24 Sturm bound 76800 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$525 = 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$24$$ Sturm bound: $$76800$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(525))$$.

Total New Old
Modular forms 29472 19286 10186
Cusp forms 28128 18874 9254
Eisenstein series 1344 412 932

## Trace form

 $$18874 q + 16 q^{2} - 37 q^{3} - 134 q^{4} + 12 q^{5} - 60 q^{6} - 146 q^{7} - 90 q^{8} - 49 q^{9} + O(q^{10})$$ $$18874 q + 16 q^{2} - 37 q^{3} - 134 q^{4} + 12 q^{5} - 60 q^{6} - 146 q^{7} - 90 q^{8} - 49 q^{9} - 248 q^{10} - 224 q^{11} + 320 q^{12} + 540 q^{13} + 216 q^{14} + 272 q^{15} + 18 q^{16} - 1132 q^{17} - 922 q^{18} - 978 q^{19} - 312 q^{20} - 393 q^{21} + 1128 q^{22} + 440 q^{23} + 300 q^{24} + 1652 q^{25} - 1254 q^{26} + 1100 q^{27} + 134 q^{28} + 3208 q^{29} + 2732 q^{30} + 2402 q^{31} + 2830 q^{32} + 1055 q^{33} - 2700 q^{34} + 208 q^{35} + 2510 q^{36} - 1758 q^{37} - 5594 q^{38} - 4500 q^{39} - 7984 q^{40} - 3872 q^{41} - 996 q^{42} + 328 q^{43} - 336 q^{44} + 2128 q^{45} + 1700 q^{46} + 2744 q^{47} + 3004 q^{48} + 234 q^{49} + 16448 q^{50} + 731 q^{51} + 7952 q^{52} + 5008 q^{53} + 2502 q^{54} - 3832 q^{55} - 20166 q^{56} - 5690 q^{57} - 26912 q^{58} - 12784 q^{59} - 2716 q^{60} + 50 q^{61} - 12724 q^{62} + 3917 q^{63} + 12214 q^{64} + 4612 q^{65} + 18762 q^{66} + 25574 q^{67} + 34448 q^{68} + 5968 q^{69} + 23204 q^{70} + 9620 q^{71} - 22722 q^{72} + 5610 q^{73} + 9638 q^{74} - 15096 q^{75} - 7848 q^{76} + 108 q^{77} - 17192 q^{78} - 14686 q^{79} - 6848 q^{80} + 4499 q^{81} - 51776 q^{82} - 39704 q^{83} - 18326 q^{84} - 41684 q^{85} - 36194 q^{86} + 864 q^{87} - 33524 q^{88} - 8556 q^{89} + 31916 q^{90} + 8224 q^{91} + 16720 q^{92} + 30871 q^{93} + 58296 q^{94} + 31888 q^{95} + 16788 q^{96} + 62284 q^{97} + 19242 q^{98} - 14694 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(525))$$

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
525.4.a $$\chi_{525}(1, \cdot)$$ 525.4.a.a 1 1
525.4.a.b 1
525.4.a.c 1
525.4.a.d 1
525.4.a.e 1
525.4.a.f 1
525.4.a.g 1
525.4.a.h 1
525.4.a.i 2
525.4.a.j 2
525.4.a.k 2
525.4.a.l 2
525.4.a.m 2
525.4.a.n 2
525.4.a.o 2
525.4.a.p 2
525.4.a.q 3
525.4.a.r 3
525.4.a.s 4
525.4.a.t 4
525.4.a.u 4
525.4.a.v 4
525.4.a.w 5
525.4.a.x 5
525.4.b $$\chi_{525}(251, \cdot)$$ n/a 146 1
525.4.d $$\chi_{525}(274, \cdot)$$ 525.4.d.a 2 1
525.4.d.b 2
525.4.d.c 2
525.4.d.d 2
525.4.d.e 2
525.4.d.f 2
525.4.d.g 4
525.4.d.h 4
525.4.d.i 4
525.4.d.j 4
525.4.d.k 4
525.4.d.l 4
525.4.d.m 4
525.4.d.n 8
525.4.d.o 8
525.4.g $$\chi_{525}(524, \cdot)$$ n/a 140 1
525.4.i $$\chi_{525}(151, \cdot)$$ n/a 152 2
525.4.j $$\chi_{525}(218, \cdot)$$ n/a 216 2
525.4.m $$\chi_{525}(118, \cdot)$$ n/a 144 2
525.4.n $$\chi_{525}(106, \cdot)$$ n/a 368 4
525.4.q $$\chi_{525}(299, \cdot)$$ n/a 280 2
525.4.r $$\chi_{525}(424, \cdot)$$ n/a 144 2
525.4.t $$\chi_{525}(26, \cdot)$$ n/a 292 2
525.4.w $$\chi_{525}(104, \cdot)$$ n/a 944 4
525.4.z $$\chi_{525}(64, \cdot)$$ n/a 352 4
525.4.bb $$\chi_{525}(41, \cdot)$$ n/a 944 4
525.4.bc $$\chi_{525}(82, \cdot)$$ n/a 288 4
525.4.bf $$\chi_{525}(32, \cdot)$$ n/a 560 4
525.4.bg $$\chi_{525}(16, \cdot)$$ n/a 960 8
525.4.bh $$\chi_{525}(13, \cdot)$$ n/a 960 8
525.4.bk $$\chi_{525}(8, \cdot)$$ n/a 1440 8
525.4.bm $$\chi_{525}(131, \cdot)$$ n/a 1888 8
525.4.bo $$\chi_{525}(4, \cdot)$$ n/a 960 8
525.4.bp $$\chi_{525}(59, \cdot)$$ n/a 1888 8
525.4.bs $$\chi_{525}(2, \cdot)$$ n/a 3776 16
525.4.bv $$\chi_{525}(52, \cdot)$$ n/a 1920 16

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(525))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(525)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 2}$$