# Properties

 Label 675.4 Level 675 Weight 4 Dimension 35064 Nonzero newspaces 18 Sturm bound 129600 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$675 = 3^{3} \cdot 5^{2}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$18$$ Sturm bound: $$129600$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(675))$$.

Total New Old
Modular forms 49440 35720 13720
Cusp forms 47760 35064 12696
Eisenstein series 1680 656 1024

## Trace form

 $$35064 q - 51 q^{2} - 78 q^{3} - 73 q^{4} - 64 q^{5} - 138 q^{6} - 125 q^{7} - 125 q^{8} - 126 q^{9} + O(q^{10})$$ $$35064 q - 51 q^{2} - 78 q^{3} - 73 q^{4} - 64 q^{5} - 138 q^{6} - 125 q^{7} - 125 q^{8} - 126 q^{9} - 64 q^{10} + 11 q^{11} + 75 q^{12} - 173 q^{13} - 377 q^{14} - 96 q^{15} - 729 q^{16} - 645 q^{17} - 711 q^{18} - 83 q^{19} + 448 q^{20} - 258 q^{21} + 1479 q^{22} + 1267 q^{23} + 1098 q^{24} - 256 q^{25} + 1194 q^{26} + 1053 q^{27} - 1558 q^{28} - 1003 q^{29} - 96 q^{30} - 1441 q^{31} - 5455 q^{32} - 2823 q^{33} - 4893 q^{34} - 2800 q^{35} - 6240 q^{36} - 593 q^{37} + 819 q^{38} + 840 q^{39} + 3488 q^{40} + 5089 q^{41} + 4146 q^{42} + 5467 q^{43} + 16787 q^{44} + 2544 q^{45} + 6733 q^{46} + 12039 q^{47} + 9897 q^{48} + 5469 q^{49} + 3416 q^{50} + 2607 q^{51} - 2669 q^{52} - 4380 q^{53} - 1242 q^{54} - 3088 q^{55} - 20491 q^{56} - 4710 q^{57} - 12869 q^{58} - 11300 q^{59} - 2688 q^{60} - 4261 q^{61} - 14594 q^{62} - 2682 q^{63} - 10547 q^{64} - 2736 q^{65} - 11235 q^{66} - 2603 q^{67} - 7060 q^{68} - 6210 q^{69} + 7840 q^{70} - 1249 q^{71} - 12396 q^{72} - 1721 q^{73} - 20645 q^{74} - 8808 q^{75} - 5397 q^{76} - 7659 q^{77} - 7422 q^{78} + 2443 q^{79} + 10248 q^{80} + 6582 q^{81} + 15342 q^{82} + 23201 q^{83} + 34506 q^{84} + 3104 q^{85} + 61433 q^{86} + 22728 q^{87} + 30655 q^{88} + 35502 q^{89} + 20196 q^{90} + 21387 q^{91} + 37769 q^{92} + 10302 q^{93} + 15543 q^{94} + 11788 q^{95} + 6090 q^{96} - 1793 q^{97} + 6022 q^{98} - 1554 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(675))$$

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
675.4.a $$\chi_{675}(1, \cdot)$$ 675.4.a.a 1 1
675.4.a.b 1
675.4.a.c 1
675.4.a.d 1
675.4.a.e 1
675.4.a.f 1
675.4.a.g 1
675.4.a.h 1
675.4.a.i 1
675.4.a.j 1
675.4.a.k 2
675.4.a.l 2
675.4.a.m 2
675.4.a.n 2
675.4.a.o 2
675.4.a.p 3
675.4.a.q 3
675.4.a.r 3
675.4.a.s 3
675.4.a.t 4
675.4.a.u 4
675.4.a.v 4
675.4.a.w 4
675.4.a.x 4
675.4.a.y 4
675.4.a.z 4
675.4.a.ba 4
675.4.a.bb 6
675.4.a.bc 6
675.4.b $$\chi_{675}(649, \cdot)$$ 675.4.b.a 2 1
675.4.b.b 2
675.4.b.c 2
675.4.b.d 2
675.4.b.e 2
675.4.b.f 2
675.4.b.g 2
675.4.b.h 2
675.4.b.i 4
675.4.b.j 4
675.4.b.k 6
675.4.b.l 6
675.4.b.m 6
675.4.b.n 6
675.4.b.o 8
675.4.b.p 8
675.4.b.q 8
675.4.e $$\chi_{675}(226, \cdot)$$ n/a 108 2
675.4.f $$\chi_{675}(107, \cdot)$$ n/a 144 2
675.4.h $$\chi_{675}(136, \cdot)$$ n/a 480 4
675.4.k $$\chi_{675}(199, \cdot)$$ n/a 104 2
675.4.l $$\chi_{675}(76, \cdot)$$ n/a 1008 6
675.4.n $$\chi_{675}(109, \cdot)$$ n/a 480 4
675.4.q $$\chi_{675}(143, \cdot)$$ n/a 208 4
675.4.r $$\chi_{675}(46, \cdot)$$ n/a 704 8
675.4.u $$\chi_{675}(49, \cdot)$$ n/a 960 6
675.4.w $$\chi_{675}(53, \cdot)$$ n/a 960 8
675.4.y $$\chi_{675}(19, \cdot)$$ n/a 704 8
675.4.ba $$\chi_{675}(32, \cdot)$$ n/a 1920 12
675.4.bc $$\chi_{675}(16, \cdot)$$ n/a 6432 24
675.4.bd $$\chi_{675}(8, \cdot)$$ n/a 1408 16
675.4.bg $$\chi_{675}(4, \cdot)$$ n/a 6432 24
675.4.bi $$\chi_{675}(2, \cdot)$$ n/a 12864 48

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(675))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(675)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 2}$$