# Properties

 Label 1425.2 Level 1425 Weight 2 Dimension 48794 Nonzero newspaces 36 Sturm bound 288000 Trace bound 7

## Defining parameters

 Level: $$N$$ = $$1425 = 3 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$288000$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1425))$$.

Total New Old
Modular forms 74016 50190 23826
Cusp forms 69985 48794 21191
Eisenstein series 4031 1396 2635

## Trace form

 $$48794 q + 2 q^{2} - 99 q^{3} - 184 q^{4} + 12 q^{5} - 143 q^{6} - 178 q^{7} + 42 q^{8} - 91 q^{9} + O(q^{10})$$ $$48794 q + 2 q^{2} - 99 q^{3} - 184 q^{4} + 12 q^{5} - 143 q^{6} - 178 q^{7} + 42 q^{8} - 91 q^{9} - 220 q^{10} + 8 q^{11} - 67 q^{12} - 150 q^{13} + 84 q^{14} - 116 q^{15} - 240 q^{16} + 22 q^{17} - 106 q^{18} - 184 q^{19} - 72 q^{20} - 156 q^{21} - 212 q^{22} - 14 q^{23} - 183 q^{24} - 316 q^{25} + 48 q^{26} - 87 q^{27} - 244 q^{28} + 8 q^{29} - 172 q^{30} - 286 q^{31} + 56 q^{32} - 43 q^{33} - 104 q^{34} + 40 q^{35} - 135 q^{36} - 124 q^{37} + 118 q^{38} - 204 q^{39} - 292 q^{40} + 80 q^{41} - 159 q^{42} - 178 q^{43} - 6 q^{44} - 272 q^{45} - 312 q^{46} + 4 q^{47} - 251 q^{48} - 292 q^{49} - 212 q^{50} - 441 q^{51} - 430 q^{52} - 112 q^{53} - 401 q^{54} - 296 q^{55} - 220 q^{57} - 520 q^{58} - 56 q^{59} - 172 q^{60} - 210 q^{61} + 82 q^{62} - 85 q^{63} + 112 q^{64} + 116 q^{65} - 73 q^{66} + 134 q^{67} + 370 q^{68} + 136 q^{69} - 8 q^{70} + 184 q^{71} + 156 q^{73} + 412 q^{74} + 84 q^{75} - 434 q^{76} + 246 q^{77} - 25 q^{78} - 118 q^{79} - 124 q^{80} - 319 q^{81} - 376 q^{82} - 250 q^{83} - 553 q^{84} - 652 q^{85} - 370 q^{86} - 521 q^{87} - 1478 q^{88} - 414 q^{89} - 456 q^{90} - 810 q^{91} - 982 q^{92} - 727 q^{93} - 1676 q^{94} - 272 q^{95} - 1524 q^{96} - 928 q^{97} - 1198 q^{98} - 676 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1425))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1425.2.a $$\chi_{1425}(1, \cdot)$$ 1425.2.a.a 1 1
1425.2.a.b 1
1425.2.a.c 1
1425.2.a.d 1
1425.2.a.e 1
1425.2.a.f 1
1425.2.a.g 1
1425.2.a.h 1
1425.2.a.i 1
1425.2.a.j 1
1425.2.a.k 2
1425.2.a.l 2
1425.2.a.m 2
1425.2.a.n 2
1425.2.a.o 2
1425.2.a.p 2
1425.2.a.q 2
1425.2.a.r 2
1425.2.a.s 3
1425.2.a.t 3
1425.2.a.u 3
1425.2.a.v 3
1425.2.a.w 3
1425.2.a.x 3
1425.2.a.y 7
1425.2.a.z 7
1425.2.b $$\chi_{1425}(1424, \cdot)$$ n/a 116 1
1425.2.c $$\chi_{1425}(799, \cdot)$$ 1425.2.c.a 2 1
1425.2.c.b 2
1425.2.c.c 2
1425.2.c.d 2
1425.2.c.e 2
1425.2.c.f 2
1425.2.c.g 2
1425.2.c.h 2
1425.2.c.i 4
1425.2.c.j 4
1425.2.c.k 4
1425.2.c.l 4
1425.2.c.m 4
1425.2.c.n 4
1425.2.c.o 6
1425.2.c.p 6
1425.2.h $$\chi_{1425}(626, \cdot)$$ n/a 120 1
1425.2.i $$\chi_{1425}(676, \cdot)$$ n/a 128 2
1425.2.k $$\chi_{1425}(818, \cdot)$$ n/a 216 2
1425.2.m $$\chi_{1425}(493, \cdot)$$ n/a 120 2
1425.2.n $$\chi_{1425}(286, \cdot)$$ n/a 352 4
1425.2.q $$\chi_{1425}(1076, \cdot)$$ n/a 240 2
1425.2.r $$\chi_{1425}(449, \cdot)$$ n/a 232 2
1425.2.s $$\chi_{1425}(49, \cdot)$$ n/a 120 2
1425.2.v $$\chi_{1425}(226, \cdot)$$ n/a 378 6
1425.2.y $$\chi_{1425}(56, \cdot)$$ n/a 784 4
1425.2.z $$\chi_{1425}(229, \cdot)$$ n/a 368 4
1425.2.ba $$\chi_{1425}(284, \cdot)$$ n/a 784 4
1425.2.bd $$\chi_{1425}(68, \cdot)$$ n/a 464 4
1425.2.bf $$\chi_{1425}(943, \cdot)$$ n/a 240 4
1425.2.bh $$\chi_{1425}(106, \cdot)$$ n/a 800 8
1425.2.bi $$\chi_{1425}(326, \cdot)$$ n/a 726 6
1425.2.bn $$\chi_{1425}(199, \cdot)$$ n/a 360 6
1425.2.bo $$\chi_{1425}(224, \cdot)$$ n/a 696 6
1425.2.bp $$\chi_{1425}(37, \cdot)$$ n/a 800 8
1425.2.br $$\chi_{1425}(77, \cdot)$$ n/a 1440 8
1425.2.bt $$\chi_{1425}(64, \cdot)$$ n/a 800 8
1425.2.bu $$\chi_{1425}(164, \cdot)$$ n/a 1568 8
1425.2.bz $$\chi_{1425}(221, \cdot)$$ n/a 1568 8
1425.2.cb $$\chi_{1425}(193, \cdot)$$ n/a 720 12
1425.2.cc $$\chi_{1425}(218, \cdot)$$ n/a 1392 12
1425.2.ce $$\chi_{1425}(16, \cdot)$$ n/a 2400 24
1425.2.cg $$\chi_{1425}(88, \cdot)$$ n/a 1600 16
1425.2.ci $$\chi_{1425}(83, \cdot)$$ n/a 3136 16
1425.2.cl $$\chi_{1425}(41, \cdot)$$ n/a 4704 24
1425.2.cm $$\chi_{1425}(14, \cdot)$$ n/a 4704 24
1425.2.cn $$\chi_{1425}(4, \cdot)$$ n/a 2400 24
1425.2.cr $$\chi_{1425}(17, \cdot)$$ n/a 9408 48
1425.2.cs $$\chi_{1425}(13, \cdot)$$ n/a 4800 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1425))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1425)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(285))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(475))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1425))$$$$^{\oplus 1}$$