# Properties

 Label 325.2 Level 325 Weight 2 Dimension 3601 Nonzero newspaces 24 Newform subspaces 78 Sturm bound 16800 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$325 = 5^{2} \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Newform subspaces: $$78$$ Sturm bound: $$16800$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(325))$$.

Total New Old
Modular forms 4536 4051 485
Cusp forms 3865 3601 264
Eisenstein series 671 450 221

## Trace form

 $$3601 q - 64 q^{2} - 66 q^{3} - 72 q^{4} - 86 q^{5} - 114 q^{6} - 76 q^{7} - 97 q^{8} - 92 q^{9} + O(q^{10})$$ $$3601 q - 64 q^{2} - 66 q^{3} - 72 q^{4} - 86 q^{5} - 114 q^{6} - 76 q^{7} - 97 q^{8} - 92 q^{9} - 106 q^{10} - 120 q^{11} - 140 q^{12} - 94 q^{13} - 196 q^{14} - 116 q^{15} - 140 q^{16} - 83 q^{17} - 119 q^{18} - 78 q^{19} - 76 q^{20} - 140 q^{21} - 80 q^{22} - 78 q^{23} - 98 q^{24} - 66 q^{25} - 270 q^{26} - 192 q^{27} - 100 q^{28} - 105 q^{29} - 116 q^{30} - 140 q^{31} - 180 q^{32} - 156 q^{33} - 164 q^{34} - 136 q^{35} - 244 q^{36} - 141 q^{37} - 160 q^{38} - 116 q^{39} - 222 q^{40} - 179 q^{41} - 140 q^{42} - 112 q^{43} - 164 q^{44} - 46 q^{45} - 198 q^{46} - 116 q^{47} + 78 q^{48} - 120 q^{49} - 34 q^{50} - 196 q^{51} + 29 q^{52} - 106 q^{53} + 148 q^{54} - 44 q^{55} + 28 q^{56} + 108 q^{57} + 43 q^{58} + 24 q^{59} + 212 q^{60} - 95 q^{61} + 174 q^{62} + 152 q^{63} + 193 q^{64} - 5 q^{65} - 36 q^{66} + 22 q^{67} + 167 q^{68} + 148 q^{69} - 12 q^{70} - 118 q^{71} + 282 q^{72} - 50 q^{73} + 27 q^{74} + 4 q^{75} - 98 q^{76} - 36 q^{77} + 8 q^{78} - 180 q^{79} - 22 q^{80} - 188 q^{81} - 157 q^{82} - 84 q^{83} - 36 q^{84} - 26 q^{85} - 240 q^{86} - 158 q^{87} - 192 q^{88} - 84 q^{89} - 46 q^{90} - 218 q^{91} - 336 q^{92} - 188 q^{93} - 170 q^{94} - 116 q^{95} - 400 q^{96} - 54 q^{97} - 224 q^{98} - 260 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(325))$$

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
325.2.a $$\chi_{325}(1, \cdot)$$ 325.2.a.a 1 1
325.2.a.b 1
325.2.a.c 1
325.2.a.d 1
325.2.a.e 1
325.2.a.f 2
325.2.a.g 2
325.2.a.h 2
325.2.a.i 2
325.2.a.j 3
325.2.a.k 3
325.2.b $$\chi_{325}(274, \cdot)$$ 325.2.b.a 2 1
325.2.b.b 2
325.2.b.c 2
325.2.b.d 4
325.2.b.e 4
325.2.b.f 4
325.2.c $$\chi_{325}(51, \cdot)$$ 325.2.c.a 2 1
325.2.c.b 2
325.2.c.c 2
325.2.c.d 2
325.2.c.e 2
325.2.c.f 2
325.2.c.g 6
325.2.d $$\chi_{325}(324, \cdot)$$ 325.2.d.a 2 1
325.2.d.b 2
325.2.d.c 2
325.2.d.d 2
325.2.d.e 6
325.2.d.f 6
325.2.e $$\chi_{325}(126, \cdot)$$ 325.2.e.a 4 2
325.2.e.b 4
325.2.e.c 10
325.2.e.d 10
325.2.e.e 12
325.2.f $$\chi_{325}(18, \cdot)$$ 325.2.f.a 2 2
325.2.f.b 8
325.2.f.c 12
325.2.f.d 16
325.2.k $$\chi_{325}(57, \cdot)$$ 325.2.k.a 2 2
325.2.k.b 8
325.2.k.c 12
325.2.k.d 16
325.2.l $$\chi_{325}(66, \cdot)$$ 325.2.l.a 4 4
325.2.l.b 56
325.2.l.c 60
325.2.m $$\chi_{325}(49, \cdot)$$ 325.2.m.a 4 2
325.2.m.b 8
325.2.m.c 8
325.2.m.d 20
325.2.n $$\chi_{325}(101, \cdot)$$ 325.2.n.a 2 2
325.2.n.b 4
325.2.n.c 4
325.2.n.d 8
325.2.n.e 10
325.2.n.f 10
325.2.o $$\chi_{325}(74, \cdot)$$ 325.2.o.a 8 2
325.2.o.b 8
325.2.o.c 20
325.2.p $$\chi_{325}(64, \cdot)$$ 325.2.p.a 128 4
325.2.q $$\chi_{325}(116, \cdot)$$ 325.2.q.a 136 4
325.2.r $$\chi_{325}(14, \cdot)$$ 325.2.r.a 120 4
325.2.s $$\chi_{325}(32, \cdot)$$ 325.2.s.a 16 4
325.2.s.b 20
325.2.s.c 40
325.2.x $$\chi_{325}(7, \cdot)$$ 325.2.x.a 16 4
325.2.x.b 20
325.2.x.c 40
325.2.y $$\chi_{325}(16, \cdot)$$ 325.2.y.a 256 8
325.2.z $$\chi_{325}(8, \cdot)$$ 325.2.z.a 8 8
325.2.z.b 256
325.2.be $$\chi_{325}(47, \cdot)$$ 325.2.be.a 8 8
325.2.be.b 256
325.2.bf $$\chi_{325}(9, \cdot)$$ 325.2.bf.a 272 8
325.2.bg $$\chi_{325}(36, \cdot)$$ 325.2.bg.a 272 8
325.2.bh $$\chi_{325}(4, \cdot)$$ 325.2.bh.a 256 8
325.2.bi $$\chi_{325}(28, \cdot)$$ 325.2.bi.a 528 16
325.2.bn $$\chi_{325}(2, \cdot)$$ 325.2.bn.a 528 16

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(325))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(325)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(325))$$$$^{\oplus 1}$$