# Properties

 Label 900.3 Level 900 Weight 3 Dimension 18202 Nonzero newspaces 24 Sturm bound 129600 Trace bound 7

## Defining parameters

 Level: $$N$$ = $$900 = 2^{2} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$24$$ Sturm bound: $$129600$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(900))$$.

Total New Old
Modular forms 44320 18572 25748
Cusp forms 42080 18202 23878
Eisenstein series 2240 370 1870

## Trace form

 $$18202 q - 17 q^{2} + 3 q^{3} - 11 q^{4} - 42 q^{5} - 49 q^{6} + 27 q^{7} - 44 q^{8} - 23 q^{9} + O(q^{10})$$ $$18202 q - 17 q^{2} + 3 q^{3} - 11 q^{4} - 42 q^{5} - 49 q^{6} + 27 q^{7} - 44 q^{8} - 23 q^{9} - 80 q^{10} + 20 q^{11} - 60 q^{12} - 29 q^{13} - 150 q^{14} - 12 q^{15} - 119 q^{16} - 126 q^{17} - 44 q^{18} - 58 q^{19} - 110 q^{20} - 251 q^{21} - 295 q^{22} - 317 q^{23} - 175 q^{24} - 252 q^{25} - 72 q^{26} - 96 q^{27} - 94 q^{28} - 277 q^{29} + 8 q^{30} + 37 q^{31} + 353 q^{32} - 110 q^{33} + 339 q^{34} - 28 q^{35} + 363 q^{36} + 348 q^{37} + 335 q^{38} - 23 q^{39} - 100 q^{40} + 80 q^{41} - 18 q^{42} - 194 q^{43} - 34 q^{44} - 224 q^{45} + 218 q^{46} - 269 q^{47} + 331 q^{48} - 815 q^{49} + 698 q^{50} + 165 q^{51} + 1190 q^{52} - 184 q^{53} + 553 q^{54} - 92 q^{55} + 1036 q^{56} + 639 q^{57} + 1072 q^{58} + 436 q^{59} - 92 q^{60} + 495 q^{61} + 672 q^{62} - 327 q^{63} - 182 q^{64} - 636 q^{65} - 314 q^{66} + 264 q^{67} - 1123 q^{68} + 697 q^{69} - 1026 q^{70} + 496 q^{71} - 229 q^{72} + 422 q^{73} - 792 q^{74} + 928 q^{75} - 1575 q^{76} + 1807 q^{77} + 1318 q^{78} - 437 q^{79} + 458 q^{80} + 617 q^{81} - 516 q^{82} + 1213 q^{83} + 726 q^{84} - 56 q^{85} + 447 q^{86} + 1445 q^{87} + 893 q^{88} + 1372 q^{89} - 184 q^{90} + 774 q^{91} + 952 q^{92} - 473 q^{93} + 2074 q^{94} + 112 q^{95} - 1156 q^{96} + 966 q^{97} + 410 q^{98} - 1109 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(900))$$

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
900.3.b $$\chi_{900}(449, \cdot)$$ 900.3.b.a 4 1
900.3.b.b 8
900.3.c $$\chi_{900}(451, \cdot)$$ 900.3.c.a 1 1
900.3.c.b 1
900.3.c.c 1
900.3.c.d 1
900.3.c.e 2
900.3.c.f 2
900.3.c.g 2
900.3.c.h 2
900.3.c.i 2
900.3.c.j 2
900.3.c.k 4
900.3.c.l 4
900.3.c.m 4
900.3.c.n 8
900.3.c.o 8
900.3.c.p 8
900.3.c.q 8
900.3.c.r 8
900.3.c.s 8
900.3.c.t 8
900.3.c.u 8
900.3.f $$\chi_{900}(199, \cdot)$$ 900.3.f.a 2 1
900.3.f.b 2
900.3.f.c 4
900.3.f.d 8
900.3.f.e 8
900.3.f.f 16
900.3.f.g 16
900.3.f.h 16
900.3.f.i 16
900.3.g $$\chi_{900}(701, \cdot)$$ 900.3.g.a 2 1
900.3.g.b 2
900.3.g.c 4
900.3.g.d 4
900.3.l $$\chi_{900}(757, \cdot)$$ 900.3.l.a 2 2
900.3.l.b 4
900.3.l.c 4
900.3.l.d 4
900.3.l.e 4
900.3.l.f 4
900.3.l.g 4
900.3.l.h 4
900.3.m $$\chi_{900}(107, \cdot)$$ n/a 144 2
900.3.p $$\chi_{900}(101, \cdot)$$ 900.3.p.a 4 2
900.3.p.b 4
900.3.p.c 12
900.3.p.d 16
900.3.p.e 16
900.3.p.f 24
900.3.q $$\chi_{900}(499, \cdot)$$ n/a 424 2
900.3.t $$\chi_{900}(151, \cdot)$$ n/a 444 2
900.3.u $$\chi_{900}(149, \cdot)$$ 900.3.u.a 8 2
900.3.u.b 8
900.3.u.c 24
900.3.u.d 32
900.3.x $$\chi_{900}(91, \cdot)$$ n/a 592 4
900.3.y $$\chi_{900}(89, \cdot)$$ 900.3.y.a 80 4
900.3.ba $$\chi_{900}(161, \cdot)$$ 900.3.ba.a 80 4
900.3.bb $$\chi_{900}(19, \cdot)$$ n/a 592 4
900.3.bc $$\chi_{900}(157, \cdot)$$ n/a 144 4
900.3.bd $$\chi_{900}(407, \cdot)$$ n/a 848 4
900.3.bh $$\chi_{900}(287, \cdot)$$ n/a 960 8
900.3.bi $$\chi_{900}(37, \cdot)$$ n/a 200 8
900.3.bl $$\chi_{900}(79, \cdot)$$ n/a 2848 8
900.3.bm $$\chi_{900}(41, \cdot)$$ n/a 480 8
900.3.bo $$\chi_{900}(29, \cdot)$$ n/a 480 8
900.3.bp $$\chi_{900}(31, \cdot)$$ n/a 2848 8
900.3.bu $$\chi_{900}(23, \cdot)$$ n/a 5696 16
900.3.bv $$\chi_{900}(13, \cdot)$$ n/a 960 16

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

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(900))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(900)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(300))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(450))$$$$^{\oplus 2}$$