# Properties

 Label 2790.2 Level 2790 Weight 2 Dimension 50054 Nonzero newspaces 60 Sturm bound 829440 Trace bound 18

## Defining parameters

 Level: $$N$$ = $$2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$60$$ Sturm bound: $$829440$$ Trace bound: $$18$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2790))$$.

Total New Old
Modular forms 211200 50054 161146
Cusp forms 203521 50054 153467
Eisenstein series 7679 0 7679

## Trace form

 $$50054 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 10 q^{5} + 12 q^{6} - 24 q^{7} + 6 q^{8} + 28 q^{9} + O(q^{10})$$ $$50054 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 10 q^{5} + 12 q^{6} - 24 q^{7} + 6 q^{8} + 28 q^{9} + 22 q^{10} + 52 q^{11} + 16 q^{12} + 28 q^{13} + 40 q^{14} + 48 q^{15} - 6 q^{16} + 36 q^{17} + 8 q^{18} + 16 q^{19} + 22 q^{20} + 72 q^{21} - 40 q^{22} + 12 q^{23} - 12 q^{24} + 14 q^{25} - 72 q^{26} + 48 q^{27} - 80 q^{28} - 108 q^{29} - 112 q^{31} - 6 q^{32} - 20 q^{33} - 128 q^{34} - 92 q^{35} - 20 q^{36} - 128 q^{37} - 144 q^{38} - 128 q^{39} + 6 q^{40} - 212 q^{41} - 128 q^{42} - 40 q^{43} - 64 q^{44} - 160 q^{45} - 120 q^{47} - 20 q^{48} - 66 q^{49} - 94 q^{50} - 60 q^{51} - 20 q^{52} - 120 q^{53} - 60 q^{54} - 20 q^{55} - 40 q^{56} - 52 q^{57} - 68 q^{58} - 80 q^{59} + 16 q^{60} - 208 q^{61} + 80 q^{63} + 6 q^{64} - 6 q^{65} + 96 q^{66} - 24 q^{67} + 72 q^{68} + 128 q^{69} + 48 q^{70} + 24 q^{71} + 12 q^{72} + 56 q^{73} + 100 q^{74} + 48 q^{75} + 152 q^{76} + 504 q^{77} + 416 q^{78} + 484 q^{79} + 80 q^{80} + 476 q^{81} + 476 q^{82} + 1188 q^{83} + 264 q^{84} + 420 q^{85} + 860 q^{86} + 520 q^{87} + 380 q^{88} + 992 q^{89} + 472 q^{90} + 908 q^{91} + 72 q^{92} + 928 q^{93} + 416 q^{94} + 696 q^{95} + 16 q^{96} + 868 q^{97} + 1134 q^{98} + 640 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2790))$$

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
2790.2.a $$\chi_{2790}(1, \cdot)$$ 2790.2.a.a 1 1
2790.2.a.b 1
2790.2.a.c 1
2790.2.a.d 1
2790.2.a.e 1
2790.2.a.f 1
2790.2.a.g 1
2790.2.a.h 1
2790.2.a.i 1
2790.2.a.j 1
2790.2.a.k 1
2790.2.a.l 1
2790.2.a.m 1
2790.2.a.n 1
2790.2.a.o 1
2790.2.a.p 1
2790.2.a.q 1
2790.2.a.r 1
2790.2.a.s 1
2790.2.a.t 1
2790.2.a.u 1
2790.2.a.v 1
2790.2.a.w 1
2790.2.a.x 1
2790.2.a.y 1
2790.2.a.z 1
2790.2.a.ba 1
2790.2.a.bb 1
2790.2.a.bc 1
2790.2.a.bd 2
2790.2.a.be 2
2790.2.a.bf 2
2790.2.a.bg 2
2790.2.a.bh 2
2790.2.a.bi 3
2790.2.a.bj 4
2790.2.a.bk 4
2790.2.d $$\chi_{2790}(559, \cdot)$$ 2790.2.d.a 2 1
2790.2.d.b 2
2790.2.d.c 2
2790.2.d.d 2
2790.2.d.e 2
2790.2.d.f 2
2790.2.d.g 2
2790.2.d.h 2
2790.2.d.i 4
2790.2.d.j 6
2790.2.d.k 6
2790.2.d.l 8
2790.2.d.m 8
2790.2.d.n 12
2790.2.d.o 16
2790.2.e $$\chi_{2790}(2789, \cdot)$$ 2790.2.e.a 32 1
2790.2.e.b 32
2790.2.h $$\chi_{2790}(2231, \cdot)$$ 2790.2.h.a 24 1
2790.2.h.b 24
2790.2.i $$\chi_{2790}(811, \cdot)$$ n/a 104 2
2790.2.j $$\chi_{2790}(931, \cdot)$$ n/a 240 2
2790.2.k $$\chi_{2790}(211, \cdot)$$ n/a 256 2
2790.2.l $$\chi_{2790}(1141, \cdot)$$ n/a 256 2
2790.2.m $$\chi_{2790}(683, \cdot)$$ n/a 120 2
2790.2.n $$\chi_{2790}(433, \cdot)$$ n/a 160 2
2790.2.q $$\chi_{2790}(721, \cdot)$$ n/a 224 4
2790.2.r $$\chi_{2790}(1699, \cdot)$$ n/a 384 2
2790.2.s $$\chi_{2790}(1049, \cdot)$$ n/a 384 2
2790.2.x $$\chi_{2790}(161, \cdot)$$ 2790.2.x.a 40 2
2790.2.x.b 40
2790.2.y $$\chi_{2790}(371, \cdot)$$ n/a 256 2
2790.2.bd $$\chi_{2790}(2021, \cdot)$$ n/a 256 2
2790.2.bg $$\chi_{2790}(929, \cdot)$$ n/a 384 2
2790.2.bh $$\chi_{2790}(719, \cdot)$$ n/a 128 2
2790.2.bi $$\chi_{2790}(1489, \cdot)$$ n/a 360 2
2790.2.bj $$\chi_{2790}(1369, \cdot)$$ n/a 160 2
2790.2.bo $$\chi_{2790}(119, \cdot)$$ n/a 384 2
2790.2.bp $$\chi_{2790}(439, \cdot)$$ n/a 384 2
2790.2.bq $$\chi_{2790}(491, \cdot)$$ n/a 256 2
2790.2.bt $$\chi_{2790}(1331, \cdot)$$ n/a 192 4
2790.2.bw $$\chi_{2790}(89, \cdot)$$ n/a 256 4
2790.2.bx $$\chi_{2790}(109, \cdot)$$ n/a 320 4
2790.2.ca $$\chi_{2790}(367, \cdot)$$ n/a 768 4
2790.2.cb $$\chi_{2790}(707, \cdot)$$ n/a 768 4
2790.2.ci $$\chi_{2790}(247, \cdot)$$ n/a 768 4
2790.2.cj $$\chi_{2790}(497, \cdot)$$ n/a 720 4
2790.2.ck $$\chi_{2790}(563, \cdot)$$ n/a 768 4
2790.2.cl $$\chi_{2790}(223, \cdot)$$ n/a 768 4
2790.2.cm $$\chi_{2790}(37, \cdot)$$ n/a 320 4
2790.2.cn $$\chi_{2790}(377, \cdot)$$ n/a 256 4
2790.2.cq $$\chi_{2790}(661, \cdot)$$ n/a 1024 8
2790.2.cr $$\chi_{2790}(121, \cdot)$$ n/a 1024 8
2790.2.cs $$\chi_{2790}(481, \cdot)$$ n/a 1024 8
2790.2.ct $$\chi_{2790}(361, \cdot)$$ n/a 416 8
2790.2.cw $$\chi_{2790}(523, \cdot)$$ n/a 640 8
2790.2.cx $$\chi_{2790}(233, \cdot)$$ n/a 512 8
2790.2.da $$\chi_{2790}(551, \cdot)$$ n/a 1024 8
2790.2.db $$\chi_{2790}(679, \cdot)$$ n/a 1536 8
2790.2.dc $$\chi_{2790}(569, \cdot)$$ n/a 1536 8
2790.2.dh $$\chi_{2790}(19, \cdot)$$ n/a 640 8
2790.2.di $$\chi_{2790}(349, \cdot)$$ n/a 1536 8
2790.2.dj $$\chi_{2790}(179, \cdot)$$ n/a 512 8
2790.2.dk $$\chi_{2790}(29, \cdot)$$ n/a 1536 8
2790.2.dn $$\chi_{2790}(11, \cdot)$$ n/a 1024 8
2790.2.ds $$\chi_{2790}(401, \cdot)$$ n/a 1024 8
2790.2.dt $$\chi_{2790}(251, \cdot)$$ n/a 320 8
2790.2.dy $$\chi_{2790}(239, \cdot)$$ n/a 1536 8
2790.2.dz $$\chi_{2790}(49, \cdot)$$ n/a 1536 8
2790.2.ec $$\chi_{2790}(107, \cdot)$$ n/a 1024 16
2790.2.ed $$\chi_{2790}(73, \cdot)$$ n/a 1280 16
2790.2.ee $$\chi_{2790}(13, \cdot)$$ n/a 3072 16
2790.2.ef $$\chi_{2790}(113, \cdot)$$ n/a 3072 16
2790.2.eg $$\chi_{2790}(47, \cdot)$$ n/a 3072 16
2790.2.eh $$\chi_{2790}(277, \cdot)$$ n/a 3072 16
2790.2.eo $$\chi_{2790}(173, \cdot)$$ n/a 3072 16
2790.2.ep $$\chi_{2790}(427, \cdot)$$ n/a 3072 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2790))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2790)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(31))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(62))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(93))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(155))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(186))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(279))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(310))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(465))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(558))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(930))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1395))$$$$^{\oplus 2}$$