# Properties

 Label 2280.2 Level 2280 Weight 2 Dimension 52756 Nonzero newspaces 54 Sturm bound 552960 Trace bound 15

## Defining parameters

 Level: $$N$$ = $$2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$54$$ Sturm bound: $$552960$$ Trace bound: $$15$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2280))$$.

Total New Old
Modular forms 141696 53572 88124
Cusp forms 134785 52756 82029
Eisenstein series 6911 816 6095

## Trace form

 $$52756 q - 8 q^{2} - 40 q^{3} - 72 q^{4} - 8 q^{5} - 84 q^{6} - 88 q^{7} + 16 q^{8} - 72 q^{9} + O(q^{10})$$ $$52756 q - 8 q^{2} - 40 q^{3} - 72 q^{4} - 8 q^{5} - 84 q^{6} - 88 q^{7} + 16 q^{8} - 72 q^{9} - 84 q^{10} + 28 q^{12} - 16 q^{13} + 64 q^{14} - 18 q^{15} - 120 q^{16} + 4 q^{18} - 32 q^{19} + 64 q^{20} + 32 q^{21} - 8 q^{22} + 48 q^{23} - 20 q^{24} - 200 q^{25} + 32 q^{26} + 38 q^{27} - 72 q^{28} - 24 q^{29} - 46 q^{30} - 144 q^{31} - 48 q^{32} - 100 q^{33} - 104 q^{34} + 24 q^{35} - 92 q^{36} + 8 q^{37} - 40 q^{38} - 140 q^{39} - 236 q^{40} - 72 q^{41} - 100 q^{42} - 168 q^{43} - 112 q^{44} - 78 q^{45} - 344 q^{46} - 104 q^{47} - 180 q^{48} - 168 q^{49} - 104 q^{50} - 246 q^{51} - 56 q^{52} - 32 q^{53} - 108 q^{54} - 76 q^{55} - 32 q^{56} - 72 q^{57} - 176 q^{58} - 48 q^{59} - 162 q^{60} - 24 q^{61} + 344 q^{62} - 128 q^{63} + 408 q^{64} + 140 q^{65} + 52 q^{66} + 312 q^{67} + 392 q^{68} + 180 q^{70} + 184 q^{71} + 36 q^{72} + 340 q^{73} + 464 q^{74} - 84 q^{75} + 472 q^{76} + 216 q^{77} + 180 q^{78} + 304 q^{79} + 128 q^{80} - 120 q^{81} + 752 q^{82} + 56 q^{83} + 252 q^{84} + 128 q^{85} + 536 q^{86} + 60 q^{87} + 600 q^{88} + 296 q^{89} - 90 q^{90} + 200 q^{91} + 376 q^{92} + 100 q^{93} + 328 q^{94} - 24 q^{95} + 8 q^{96} - 96 q^{97} + 200 q^{98} - 86 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2280))$$

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
2280.2.a $$\chi_{2280}(1, \cdot)$$ 2280.2.a.a 1 1
2280.2.a.b 1
2280.2.a.c 1
2280.2.a.d 1
2280.2.a.e 1
2280.2.a.f 1
2280.2.a.g 1
2280.2.a.h 1
2280.2.a.i 1
2280.2.a.j 1
2280.2.a.k 2
2280.2.a.l 2
2280.2.a.m 2
2280.2.a.n 2
2280.2.a.o 2
2280.2.a.p 2
2280.2.a.q 2
2280.2.a.r 3
2280.2.a.s 3
2280.2.a.t 3
2280.2.a.u 3
2280.2.c $$\chi_{2280}(1331, \cdot)$$ n/a 288 1
2280.2.d $$\chi_{2280}(151, \cdot)$$ None 0 1
2280.2.f $$\chi_{2280}(229, \cdot)$$ n/a 216 1
2280.2.i $$\chi_{2280}(569, \cdot)$$ n/a 120 1
2280.2.j $$\chi_{2280}(1369, \cdot)$$ 2280.2.j.a 2 1
2280.2.j.b 2
2280.2.j.c 2
2280.2.j.d 2
2280.2.j.e 2
2280.2.j.f 6
2280.2.j.g 10
2280.2.j.h 12
2280.2.j.i 18
2280.2.m $$\chi_{2280}(1709, \cdot)$$ n/a 472 1
2280.2.o $$\chi_{2280}(191, \cdot)$$ None 0 1
2280.2.p $$\chi_{2280}(1291, \cdot)$$ n/a 160 1
2280.2.r $$\chi_{2280}(1481, \cdot)$$ 2280.2.r.a 40 1
2280.2.r.b 40
2280.2.u $$\chi_{2280}(1141, \cdot)$$ n/a 144 1
2280.2.w $$\chi_{2280}(1519, \cdot)$$ None 0 1
2280.2.x $$\chi_{2280}(419, \cdot)$$ n/a 432 1
2280.2.ba $$\chi_{2280}(379, \cdot)$$ n/a 240 1
2280.2.bb $$\chi_{2280}(1559, \cdot)$$ None 0 1
2280.2.bd $$\chi_{2280}(341, \cdot)$$ n/a 320 1
2280.2.bg $$\chi_{2280}(121, \cdot)$$ 2280.2.bg.a 2 2
2280.2.bg.b 2
2280.2.bg.c 2
2280.2.bg.d 2
2280.2.bg.e 2
2280.2.bg.f 2
2280.2.bg.g 2
2280.2.bg.h 2
2280.2.bg.i 2
2280.2.bg.j 2
2280.2.bg.k 2
2280.2.bg.l 4
2280.2.bg.m 4
2280.2.bg.n 4
2280.2.bg.o 4
2280.2.bg.p 4
2280.2.bg.q 4
2280.2.bg.r 4
2280.2.bg.s 6
2280.2.bg.t 8
2280.2.bg.u 8
2280.2.bg.v 8
2280.2.bh $$\chi_{2280}(37, \cdot)$$ n/a 480 2
2280.2.bk $$\chi_{2280}(343, \cdot)$$ None 0 2
2280.2.bm $$\chi_{2280}(1217, \cdot)$$ n/a 216 2
2280.2.bn $$\chi_{2280}(227, \cdot)$$ n/a 944 2
2280.2.bp $$\chi_{2280}(77, \cdot)$$ n/a 864 2
2280.2.bs $$\chi_{2280}(1367, \cdot)$$ None 0 2
2280.2.bu $$\chi_{2280}(1177, \cdot)$$ n/a 120 2
2280.2.bv $$\chi_{2280}(1027, \cdot)$$ n/a 432 2
2280.2.bx $$\chi_{2280}(449, \cdot)$$ n/a 240 2
2280.2.ca $$\chi_{2280}(349, \cdot)$$ n/a 480 2
2280.2.cc $$\chi_{2280}(31, \cdot)$$ None 0 2
2280.2.cd $$\chi_{2280}(11, \cdot)$$ n/a 640 2
2280.2.cg $$\chi_{2280}(331, \cdot)$$ n/a 320 2
2280.2.ch $$\chi_{2280}(311, \cdot)$$ None 0 2
2280.2.cj $$\chi_{2280}(749, \cdot)$$ n/a 944 2
2280.2.cm $$\chi_{2280}(49, \cdot)$$ n/a 120 2
2280.2.co $$\chi_{2280}(539, \cdot)$$ n/a 944 2
2280.2.cp $$\chi_{2280}(559, \cdot)$$ None 0 2
2280.2.cr $$\chi_{2280}(1261, \cdot)$$ n/a 320 2
2280.2.cu $$\chi_{2280}(521, \cdot)$$ n/a 160 2
2280.2.cx $$\chi_{2280}(221, \cdot)$$ n/a 640 2
2280.2.cz $$\chi_{2280}(239, \cdot)$$ None 0 2
2280.2.da $$\chi_{2280}(259, \cdot)$$ n/a 480 2
2280.2.dc $$\chi_{2280}(481, \cdot)$$ n/a 240 6
2280.2.de $$\chi_{2280}(107, \cdot)$$ n/a 1888 4
2280.2.df $$\chi_{2280}(353, \cdot)$$ n/a 480 4
2280.2.dh $$\chi_{2280}(7, \cdot)$$ None 0 4
2280.2.dk $$\chi_{2280}(373, \cdot)$$ n/a 960 4
2280.2.dm $$\chi_{2280}(163, \cdot)$$ n/a 960 4
2280.2.dn $$\chi_{2280}(217, \cdot)$$ n/a 240 4
2280.2.dp $$\chi_{2280}(407, \cdot)$$ None 0 4
2280.2.ds $$\chi_{2280}(197, \cdot)$$ n/a 1888 4
2280.2.du $$\chi_{2280}(979, \cdot)$$ n/a 1440 6
2280.2.dx $$\chi_{2280}(119, \cdot)$$ None 0 6
2280.2.dy $$\chi_{2280}(941, \cdot)$$ n/a 1920 6
2280.2.eb $$\chi_{2280}(61, \cdot)$$ n/a 960 6
2280.2.ec $$\chi_{2280}(79, \cdot)$$ None 0 6
2280.2.ef $$\chi_{2280}(41, \cdot)$$ n/a 480 6
2280.2.eg $$\chi_{2280}(899, \cdot)$$ n/a 2832 6
2280.2.ej $$\chi_{2280}(169, \cdot)$$ n/a 360 6
2280.2.ek $$\chi_{2280}(91, \cdot)$$ n/a 960 6
2280.2.en $$\chi_{2280}(29, \cdot)$$ n/a 2832 6
2280.2.eo $$\chi_{2280}(671, \cdot)$$ None 0 6
2280.2.er $$\chi_{2280}(751, \cdot)$$ None 0 6
2280.2.es $$\chi_{2280}(709, \cdot)$$ n/a 1440 6
2280.2.ev $$\chi_{2280}(131, \cdot)$$ n/a 1920 6
2280.2.ew $$\chi_{2280}(89, \cdot)$$ n/a 720 6
2280.2.ez $$\chi_{2280}(143, \cdot)$$ None 0 12
2280.2.fa $$\chi_{2280}(557, \cdot)$$ n/a 5664 12
2280.2.fd $$\chi_{2280}(97, \cdot)$$ n/a 720 12
2280.2.fe $$\chi_{2280}(43, \cdot)$$ n/a 2880 12
2280.2.fg $$\chi_{2280}(17, \cdot)$$ n/a 1440 12
2280.2.fj $$\chi_{2280}(203, \cdot)$$ n/a 5664 12
2280.2.fk $$\chi_{2280}(367, \cdot)$$ None 0 12
2280.2.fn $$\chi_{2280}(13, \cdot)$$ n/a 2880 12

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2280))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2280)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(228))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(285))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(380))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(456))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(570))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(760))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1140))$$$$^{\oplus 2}$$