# Properties

 Label 2394.2 Level 2394 Weight 2 Dimension 39110 Nonzero newspaces 92 Sturm bound 622080 Trace bound 22

## Defining parameters

 Level: $$N$$ = $$2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$92$$ Sturm bound: $$622080$$ Trace bound: $$22$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2394))$$.

Total New Old
Modular forms 158976 39110 119866
Cusp forms 152065 39110 112955
Eisenstein series 6911 0 6911

## Trace form

 $$39110 q - 4 q^{2} - 12 q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} - 20 q^{7} + 8 q^{8} + 12 q^{9} + O(q^{10})$$ $$39110 q - 4 q^{2} - 12 q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} - 20 q^{7} + 8 q^{8} + 12 q^{9} - 12 q^{10} - 12 q^{11} - 60 q^{13} + 14 q^{14} + 48 q^{15} + 8 q^{16} + 36 q^{17} + 24 q^{18} - 54 q^{19} + 84 q^{21} + 30 q^{22} + 84 q^{23} + 12 q^{24} + 8 q^{25} + 40 q^{26} + 72 q^{27} + 2 q^{28} - 12 q^{29} + 24 q^{30} - 12 q^{31} - 4 q^{32} + 12 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} - 52 q^{37} - 16 q^{38} + 72 q^{39} - 12 q^{40} + 24 q^{41} - 40 q^{43} + 6 q^{44} + 312 q^{45} + 120 q^{46} + 384 q^{47} + 48 q^{48} + 38 q^{49} + 332 q^{50} + 324 q^{51} + 48 q^{52} + 384 q^{53} + 108 q^{54} + 432 q^{55} + 92 q^{56} + 270 q^{57} + 240 q^{58} + 300 q^{59} + 432 q^{61} + 124 q^{62} - 216 q^{63} + 40 q^{64} + 168 q^{65} + 96 q^{66} + 232 q^{67} - 54 q^{68} + 144 q^{70} + 48 q^{71} + 48 q^{72} + 30 q^{73} - 128 q^{74} - 228 q^{75} - 168 q^{77} - 120 q^{78} - 164 q^{79} - 12 q^{80} - 12 q^{81} - 72 q^{82} - 204 q^{83} - 12 q^{84} - 264 q^{85} - 92 q^{86} + 216 q^{87} + 36 q^{88} + 24 q^{89} + 96 q^{90} + 36 q^{91} + 216 q^{93} - 48 q^{94} + 252 q^{95} + 24 q^{96} + 216 q^{97} + 80 q^{98} + 564 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2394))$$

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
2394.2.a $$\chi_{2394}(1, \cdot)$$ 2394.2.a.a 1 1
2394.2.a.b 1
2394.2.a.c 1
2394.2.a.d 1
2394.2.a.e 1
2394.2.a.f 1
2394.2.a.g 1
2394.2.a.h 1
2394.2.a.i 1
2394.2.a.j 1
2394.2.a.k 1
2394.2.a.l 1
2394.2.a.m 1
2394.2.a.n 1
2394.2.a.o 1
2394.2.a.p 2
2394.2.a.q 2
2394.2.a.r 2
2394.2.a.s 2
2394.2.a.t 2
2394.2.a.u 2
2394.2.a.v 2
2394.2.a.w 2
2394.2.a.x 2
2394.2.a.y 2
2394.2.a.z 2
2394.2.a.ba 3
2394.2.a.bb 3
2394.2.a.bc 3
2394.2.b $$\chi_{2394}(1709, \cdot)$$ 2394.2.b.a 2 1
2394.2.b.b 2
2394.2.b.c 2
2394.2.b.d 2
2394.2.b.e 2
2394.2.b.f 2
2394.2.b.g 6
2394.2.b.h 6
2394.2.b.i 8
2394.2.b.j 8
2394.2.e $$\chi_{2394}(1063, \cdot)$$ 2394.2.e.a 12 1
2394.2.e.b 12
2394.2.e.c 16
2394.2.e.d 24
2394.2.f $$\chi_{2394}(2015, \cdot)$$ 2394.2.f.a 24 1
2394.2.f.b 24
2394.2.i $$\chi_{2394}(1255, \cdot)$$ n/a 288 2
2394.2.j $$\chi_{2394}(121, \cdot)$$ n/a 320 2
2394.2.k $$\chi_{2394}(799, \cdot)$$ n/a 216 2
2394.2.l $$\chi_{2394}(163, \cdot)$$ n/a 136 2
2394.2.m $$\chi_{2394}(1369, \cdot)$$ n/a 120 2
2394.2.n $$\chi_{2394}(2059, \cdot)$$ n/a 240 2
2394.2.o $$\chi_{2394}(505, \cdot)$$ 2394.2.o.a 2 2
2394.2.o.b 2
2394.2.o.c 2
2394.2.o.d 2
2394.2.o.e 2
2394.2.o.f 2
2394.2.o.g 2
2394.2.o.h 2
2394.2.o.i 2
2394.2.o.j 2
2394.2.o.k 4
2394.2.o.l 4
2394.2.o.m 4
2394.2.o.n 4
2394.2.o.o 4
2394.2.o.p 4
2394.2.o.q 4
2394.2.o.r 6
2394.2.o.s 6
2394.2.o.t 6
2394.2.o.u 6
2394.2.o.v 8
2394.2.o.w 10
2394.2.o.x 10
2394.2.p $$\chi_{2394}(961, \cdot)$$ n/a 320 2
2394.2.q $$\chi_{2394}(1075, \cdot)$$ n/a 320 2
2394.2.r $$\chi_{2394}(919, \cdot)$$ n/a 136 2
2394.2.s $$\chi_{2394}(463, \cdot)$$ n/a 240 2
2394.2.t $$\chi_{2394}(1033, \cdot)$$ n/a 320 2
2394.2.u $$\chi_{2394}(457, \cdot)$$ n/a 288 2
2394.2.w $$\chi_{2394}(569, \cdot)$$ n/a 320 2
2394.2.y $$\chi_{2394}(1357, \cdot)$$ n/a 320 2
2394.2.z $$\chi_{2394}(145, \cdot)$$ n/a 136 2
2394.2.bc $$\chi_{2394}(103, \cdot)$$ n/a 320 2
2394.2.bd $$\chi_{2394}(1019, \cdot)$$ n/a 320 2
2394.2.bg $$\chi_{2394}(107, \cdot)$$ n/a 112 2
2394.2.bh $$\chi_{2394}(407, \cdot)$$ n/a 240 2
2394.2.bj $$\chi_{2394}(1291, \cdot)$$ n/a 320 2
2394.2.bl $$\chi_{2394}(425, \cdot)$$ n/a 320 2
2394.2.bo $$\chi_{2394}(125, \cdot)$$ 2394.2.bo.a 96 2
2394.2.bp $$\chi_{2394}(311, \cdot)$$ n/a 320 2
2394.2.bx $$\chi_{2394}(83, \cdot)$$ n/a 320 2
2394.2.by $$\chi_{2394}(647, \cdot)$$ 2394.2.by.a 48 2
2394.2.by.b 48
2394.2.cd $$\chi_{2394}(353, \cdot)$$ n/a 320 2
2394.2.ce $$\chi_{2394}(761, \cdot)$$ n/a 288 2
2394.2.cf $$\chi_{2394}(467, \cdot)$$ n/a 112 2
2394.2.cg $$\chi_{2394}(419, \cdot)$$ n/a 288 2
2394.2.cm $$\chi_{2394}(977, \cdot)$$ n/a 320 2
2394.2.cp $$\chi_{2394}(65, \cdot)$$ n/a 320 2
2394.2.cq $$\chi_{2394}(449, \cdot)$$ 2394.2.cq.a 4 2
2394.2.cq.b 4
2394.2.cq.c 16
2394.2.cq.d 16
2394.2.cq.e 20
2394.2.cq.f 20
2394.2.cu $$\chi_{2394}(265, \cdot)$$ n/a 320 2
2394.2.cv $$\chi_{2394}(829, \cdot)$$ n/a 136 2
2394.2.cw $$\chi_{2394}(493, \cdot)$$ n/a 320 2
2394.2.cx $$\chi_{2394}(1741, \cdot)$$ n/a 320 2
2394.2.dc $$\chi_{2394}(1405, \cdot)$$ n/a 136 2
2394.2.dd $$\chi_{2394}(601, \cdot)$$ n/a 320 2
2394.2.de $$\chi_{2394}(2003, \cdot)$$ n/a 240 2
2394.2.df $$\chi_{2394}(683, \cdot)$$ n/a 112 2
2394.2.dk $$\chi_{2394}(863, \cdot)$$ n/a 112 2
2394.2.dl $$\chi_{2394}(113, \cdot)$$ n/a 240 2
2394.2.dm $$\chi_{2394}(905, \cdot)$$ n/a 320 2
2394.2.dn $$\chi_{2394}(2165, \cdot)$$ n/a 320 2
2394.2.dr $$\chi_{2394}(31, \cdot)$$ n/a 320 2
2394.2.ds $$\chi_{2394}(559, \cdot)$$ n/a 128 2
2394.2.dv $$\chi_{2394}(787, \cdot)$$ n/a 320 2
2394.2.dx $$\chi_{2394}(1445, \cdot)$$ n/a 288 2
2394.2.eb $$\chi_{2394}(1109, \cdot)$$ n/a 320 2
2394.2.ee $$\chi_{2394}(1679, \cdot)$$ n/a 320 2
2394.2.ef $$\chi_{2394}(1151, \cdot)$$ n/a 112 2
2394.2.ei $$\chi_{2394}(709, \cdot)$$ n/a 960 6
2394.2.ej $$\chi_{2394}(25, \cdot)$$ n/a 960 6
2394.2.ek $$\chi_{2394}(253, \cdot)$$ n/a 300 6
2394.2.el $$\chi_{2394}(43, \cdot)$$ n/a 720 6
2394.2.em $$\chi_{2394}(289, \cdot)$$ n/a 396 6
2394.2.en $$\chi_{2394}(823, \cdot)$$ n/a 960 6
2394.2.eo $$\chi_{2394}(415, \cdot)$$ n/a 396 6
2394.2.ep $$\chi_{2394}(529, \cdot)$$ n/a 960 6
2394.2.eq $$\chi_{2394}(841, \cdot)$$ n/a 720 6
2394.2.er $$\chi_{2394}(29, \cdot)$$ n/a 720 6
2394.2.es $$\chi_{2394}(1175, \cdot)$$ n/a 960 6
2394.2.ex $$\chi_{2394}(719, \cdot)$$ n/a 312 6
2394.2.ey $$\chi_{2394}(605, \cdot)$$ n/a 960 6
2394.2.ez $$\chi_{2394}(515, \cdot)$$ n/a 960 6
2394.2.fa $$\chi_{2394}(53, \cdot)$$ n/a 312 6
2394.2.fh $$\chi_{2394}(13, \cdot)$$ n/a 960 6
2394.2.fi $$\chi_{2394}(181, \cdot)$$ n/a 408 6
2394.2.fj $$\chi_{2394}(535, \cdot)$$ n/a 960 6
2394.2.fk $$\chi_{2394}(241, \cdot)$$ n/a 960 6
2394.2.ft $$\chi_{2394}(409, \cdot)$$ n/a 960 6
2394.2.fu $$\chi_{2394}(325, \cdot)$$ n/a 396 6
2394.2.fv $$\chi_{2394}(17, \cdot)$$ n/a 312 6
2394.2.fw $$\chi_{2394}(803, \cdot)$$ n/a 960 6
2394.2.fx $$\chi_{2394}(599, \cdot)$$ n/a 960 6
2394.2.fy $$\chi_{2394}(485, \cdot)$$ n/a 312 6
2394.2.gh $$\chi_{2394}(155, \cdot)$$ n/a 720 6
2394.2.gi $$\chi_{2394}(71, \cdot)$$ n/a 240 6
2394.2.gj $$\chi_{2394}(5, \cdot)$$ n/a 960 6
2394.2.gk $$\chi_{2394}(47, \cdot)$$ n/a 960 6
2394.2.gl $$\chi_{2394}(401, \cdot)$$ n/a 960 6
2394.2.gm $$\chi_{2394}(317, \cdot)$$ n/a 960 6
2394.2.gn $$\chi_{2394}(251, \cdot)$$ n/a 336 6
2394.2.go $$\chi_{2394}(461, \cdot)$$ n/a 960 6
2394.2.gv $$\chi_{2394}(355, \cdot)$$ n/a 960 6
2394.2.gw $$\chi_{2394}(649, \cdot)$$ n/a 396 6
2394.2.hb $$\chi_{2394}(895, \cdot)$$ n/a 960 6

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2394))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2394)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(133))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(171))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(266))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(342))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(399))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(798))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1197))$$$$^{\oplus 2}$$