# Properties

 Label 1260.2 Level 1260 Weight 2 Dimension 16558 Nonzero newspaces 60 Sturm bound 165888 Trace bound 25

## Defining parameters

 Level: $$N$$ = $$1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$60$$ Sturm bound: $$165888$$ Trace bound: $$25$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1260))$$.

Total New Old
Modular forms 43392 17094 26298
Cusp forms 39553 16558 22995
Eisenstein series 3839 536 3303

## Trace form

 $$16558 q - 18 q^{2} - 30 q^{4} - 43 q^{5} - 52 q^{6} - 42 q^{8} - 72 q^{9} + O(q^{10})$$ $$16558 q - 18 q^{2} - 30 q^{4} - 43 q^{5} - 52 q^{6} - 42 q^{8} - 72 q^{9} - 78 q^{10} - 50 q^{11} + 16 q^{12} - 108 q^{13} - 6 q^{14} - 18 q^{15} - 18 q^{16} - 86 q^{17} + 80 q^{18} - 82 q^{19} + 98 q^{20} - 154 q^{21} + 72 q^{22} - 18 q^{23} + 60 q^{24} - 59 q^{25} + 148 q^{26} + 12 q^{27} + 50 q^{28} - 24 q^{29} + 54 q^{30} + 38 q^{31} + 122 q^{32} + 156 q^{33} + 216 q^{34} + 77 q^{35} - 60 q^{36} - 10 q^{37} + 160 q^{38} + 172 q^{39} + 162 q^{40} + 272 q^{41} + 92 q^{42} + 112 q^{43} + 204 q^{44} + 198 q^{45} + 128 q^{46} + 234 q^{47} + 164 q^{48} + 120 q^{49} - 10 q^{50} + 240 q^{51} + 152 q^{52} + 358 q^{53} + 80 q^{54} + 94 q^{55} + 70 q^{56} + 200 q^{57} + 44 q^{58} + 202 q^{59} - 122 q^{60} + 86 q^{61} - 128 q^{62} + 166 q^{63} - 114 q^{64} + 242 q^{65} - 284 q^{66} - 34 q^{67} - 280 q^{68} + 76 q^{69} + 6 q^{70} + 24 q^{71} - 432 q^{72} + 90 q^{73} - 468 q^{74} - 42 q^{75} - 152 q^{76} + 276 q^{77} - 520 q^{78} + 102 q^{79} - 350 q^{80} - 72 q^{81} - 52 q^{82} - 24 q^{83} - 340 q^{84} + 150 q^{85} - 404 q^{86} - 152 q^{87} - 168 q^{88} + 266 q^{89} - 426 q^{90} + 128 q^{91} - 484 q^{92} + 184 q^{93} - 156 q^{94} + 69 q^{95} - 448 q^{96} + 436 q^{97} - 342 q^{98} - 44 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1260))$$

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
1260.2.a $$\chi_{1260}(1, \cdot)$$ 1260.2.a.a 1 1
1260.2.a.b 1
1260.2.a.c 1
1260.2.a.d 1
1260.2.a.e 1
1260.2.a.f 1
1260.2.a.g 1
1260.2.a.h 1
1260.2.a.i 1
1260.2.a.j 1
1260.2.c $$\chi_{1260}(811, \cdot)$$ 1260.2.c.a 4 1
1260.2.c.b 4
1260.2.c.c 8
1260.2.c.d 16
1260.2.c.e 16
1260.2.c.f 32
1260.2.d $$\chi_{1260}(881, \cdot)$$ 1260.2.d.a 4 1
1260.2.d.b 4
1260.2.f $$\chi_{1260}(629, \cdot)$$ 1260.2.f.a 8 1
1260.2.f.b 8
1260.2.i $$\chi_{1260}(559, \cdot)$$ n/a 116 1
1260.2.k $$\chi_{1260}(1009, \cdot)$$ 1260.2.k.a 2 1
1260.2.k.b 2
1260.2.k.c 2
1260.2.k.d 2
1260.2.k.e 8
1260.2.l $$\chi_{1260}(1079, \cdot)$$ 1260.2.l.a 4 1
1260.2.l.b 4
1260.2.l.c 32
1260.2.l.d 32
1260.2.n $$\chi_{1260}(71, \cdot)$$ 1260.2.n.a 24 1
1260.2.n.b 24
1260.2.q $$\chi_{1260}(121, \cdot)$$ 1260.2.q.a 2 2
1260.2.q.b 2
1260.2.q.c 2
1260.2.q.d 26
1260.2.q.e 32
1260.2.r $$\chi_{1260}(421, \cdot)$$ 1260.2.r.a 2 2
1260.2.r.b 2
1260.2.r.c 2
1260.2.r.d 2
1260.2.r.e 2
1260.2.r.f 8
1260.2.r.g 8
1260.2.r.h 8
1260.2.r.i 14
1260.2.s $$\chi_{1260}(361, \cdot)$$ 1260.2.s.a 2 2
1260.2.s.b 2
1260.2.s.c 2
1260.2.s.d 2
1260.2.s.e 4
1260.2.s.f 4
1260.2.s.g 6
1260.2.s.h 6
1260.2.t $$\chi_{1260}(961, \cdot)$$ 1260.2.t.a 2 2
1260.2.t.b 2
1260.2.t.c 2
1260.2.t.d 26
1260.2.t.e 32
1260.2.v $$\chi_{1260}(197, \cdot)$$ 1260.2.v.a 12 2
1260.2.v.b 12
1260.2.w $$\chi_{1260}(127, \cdot)$$ n/a 180 2
1260.2.z $$\chi_{1260}(503, \cdot)$$ n/a 192 2
1260.2.ba $$\chi_{1260}(433, \cdot)$$ 1260.2.ba.a 8 2
1260.2.ba.b 16
1260.2.ba.c 16
1260.2.bc $$\chi_{1260}(439, \cdot)$$ n/a 560 2
1260.2.bf $$\chi_{1260}(689, \cdot)$$ 1260.2.bf.a 96 2
1260.2.bh $$\chi_{1260}(941, \cdot)$$ 1260.2.bh.a 2 2
1260.2.bh.b 2
1260.2.bh.c 2
1260.2.bh.d 28
1260.2.bh.e 30
1260.2.bi $$\chi_{1260}(31, \cdot)$$ n/a 384 2
1260.2.bl $$\chi_{1260}(179, \cdot)$$ n/a 192 2
1260.2.bm $$\chi_{1260}(109, \cdot)$$ 1260.2.bm.a 4 2
1260.2.bm.b 4
1260.2.bm.c 16
1260.2.bm.d 16
1260.2.bo $$\chi_{1260}(491, \cdot)$$ n/a 288 2
1260.2.bs $$\chi_{1260}(11, \cdot)$$ n/a 384 2
1260.2.bv $$\chi_{1260}(169, \cdot)$$ 1260.2.bv.a 4 2
1260.2.bv.b 68
1260.2.bx $$\chi_{1260}(779, \cdot)$$ n/a 560 2
1260.2.by $$\chi_{1260}(529, \cdot)$$ 1260.2.by.a 4 2
1260.2.by.b 92
1260.2.ca $$\chi_{1260}(239, \cdot)$$ n/a 432 2
1260.2.ce $$\chi_{1260}(431, \cdot)$$ n/a 128 2
1260.2.cg $$\chi_{1260}(341, \cdot)$$ 1260.2.cg.a 12 2
1260.2.cg.b 12
1260.2.ch $$\chi_{1260}(271, \cdot)$$ n/a 160 2
1260.2.cj $$\chi_{1260}(209, \cdot)$$ 1260.2.cj.a 8 2
1260.2.cj.b 8
1260.2.cj.c 80
1260.2.cl $$\chi_{1260}(619, \cdot)$$ n/a 560 2
1260.2.co $$\chi_{1260}(509, \cdot)$$ 1260.2.co.a 96 2
1260.2.cq $$\chi_{1260}(139, \cdot)$$ n/a 560 2
1260.2.cs $$\chi_{1260}(391, \cdot)$$ n/a 384 2
1260.2.cu $$\chi_{1260}(101, \cdot)$$ 1260.2.cu.a 2 2
1260.2.cu.b 2
1260.2.cu.c 2
1260.2.cu.d 28
1260.2.cu.e 30
1260.2.cv $$\chi_{1260}(871, \cdot)$$ n/a 384 2
1260.2.cx $$\chi_{1260}(41, \cdot)$$ 1260.2.cx.a 2 2
1260.2.cx.b 2
1260.2.cx.c 30
1260.2.cx.d 30
1260.2.cz $$\chi_{1260}(19, \cdot)$$ n/a 232 2
1260.2.dc $$\chi_{1260}(89, \cdot)$$ 1260.2.dc.a 32 2
1260.2.df $$\chi_{1260}(191, \cdot)$$ n/a 384 2
1260.2.dh $$\chi_{1260}(599, \cdot)$$ n/a 560 2
1260.2.di $$\chi_{1260}(709, \cdot)$$ 1260.2.di.a 4 2
1260.2.di.b 92
1260.2.dl $$\chi_{1260}(67, \cdot)$$ n/a 1120 4
1260.2.dm $$\chi_{1260}(317, \cdot)$$ n/a 192 4
1260.2.do $$\chi_{1260}(83, \cdot)$$ n/a 1120 4
1260.2.dq $$\chi_{1260}(73, \cdot)$$ 1260.2.dq.a 16 4
1260.2.dq.b 32
1260.2.dq.c 32
1260.2.ds $$\chi_{1260}(493, \cdot)$$ n/a 192 4
1260.2.dv $$\chi_{1260}(227, \cdot)$$ n/a 1120 4
1260.2.dx $$\chi_{1260}(143, \cdot)$$ n/a 384 4
1260.2.dz $$\chi_{1260}(13, \cdot)$$ n/a 192 4
1260.2.ea $$\chi_{1260}(113, \cdot)$$ n/a 144 4
1260.2.ec $$\chi_{1260}(163, \cdot)$$ n/a 464 4
1260.2.ee $$\chi_{1260}(247, \cdot)$$ n/a 1120 4
1260.2.eh $$\chi_{1260}(137, \cdot)$$ n/a 192 4
1260.2.ej $$\chi_{1260}(53, \cdot)$$ 1260.2.ej.a 64 4
1260.2.el $$\chi_{1260}(43, \cdot)$$ n/a 864 4
1260.2.en $$\chi_{1260}(157, \cdot)$$ n/a 192 4
1260.2.eo $$\chi_{1260}(47, \cdot)$$ n/a 1120 4

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1260))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1260)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(210))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(252))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(315))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(420))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(630))$$$$^{\oplus 2}$$