# Properties

 Label 2394.4 Level 2394 Weight 4 Dimension 117334 Nonzero newspaces 92 Sturm bound 1244160 Trace bound 19

## Defining parameters

 Level: $$N$$ = $$2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$92$$ Sturm bound: $$1244160$$ Trace bound: $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(2394))$$.

Total New Old
Modular forms 470016 117334 352682
Cusp forms 463104 117334 345770
Eisenstein series 6912 0 6912

## Trace form

 $$117334 q + 16 q^{2} + 12 q^{3} - 32 q^{4} + 96 q^{5} - 72 q^{6} + 88 q^{7} - 32 q^{8} - 420 q^{9} + O(q^{10})$$ $$117334 q + 16 q^{2} + 12 q^{3} - 32 q^{4} + 96 q^{5} - 72 q^{6} + 88 q^{7} - 32 q^{8} - 420 q^{9} - 120 q^{10} + 24 q^{11} + 96 q^{12} - 76 q^{13} + 892 q^{14} + 840 q^{15} - 128 q^{16} - 84 q^{17} - 48 q^{18} + 1024 q^{19} + 48 q^{20} - 1512 q^{21} - 1140 q^{22} - 3228 q^{23} - 288 q^{24} - 3380 q^{25} - 2368 q^{26} + 1584 q^{27} - 416 q^{28} + 1068 q^{29} + 528 q^{30} + 3776 q^{31} + 256 q^{32} + 4548 q^{33} + 2184 q^{34} + 4956 q^{35} + 2064 q^{36} + 1016 q^{37} + 616 q^{38} - 4848 q^{39} - 480 q^{40} - 6384 q^{41} - 1632 q^{42} + 2636 q^{43} + 3624 q^{44} + 10824 q^{45} + 12672 q^{46} + 5304 q^{47} + 4738 q^{49} - 8864 q^{50} - 16524 q^{51} + 224 q^{52} - 14916 q^{53} - 8424 q^{54} - 25128 q^{55} - 5600 q^{56} - 15114 q^{57} - 14928 q^{58} - 19140 q^{59} - 2016 q^{60} - 28612 q^{61} - 10072 q^{62} + 15228 q^{63} + 1024 q^{64} + 21564 q^{65} + 20544 q^{66} + 23120 q^{67} + 10248 q^{68} + 35424 q^{69} + 15216 q^{70} + 55092 q^{71} + 6528 q^{72} + 17570 q^{73} - 2608 q^{74} - 10428 q^{75} + 256 q^{76} - 19746 q^{77} - 16560 q^{78} - 13984 q^{79} - 1920 q^{80} - 588 q^{81} - 14496 q^{82} - 13944 q^{83} + 1488 q^{84} - 10272 q^{85} + 10568 q^{86} - 3384 q^{87} + 4704 q^{88} + 12960 q^{89} + 8448 q^{90} + 15884 q^{91} + 5280 q^{92} - 5496 q^{93} + 19536 q^{94} + 58242 q^{95} + 768 q^{96} + 48788 q^{97} - 440 q^{98} + 22380 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(2394))$$

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
2394.4.a $$\chi_{2394}(1, \cdot)$$ 2394.4.a.a 1 1
2394.4.a.b 1
2394.4.a.c 1
2394.4.a.d 1
2394.4.a.e 1
2394.4.a.f 2
2394.4.a.g 2
2394.4.a.h 2
2394.4.a.i 2
2394.4.a.j 2
2394.4.a.k 3
2394.4.a.l 3
2394.4.a.m 3
2394.4.a.n 3
2394.4.a.o 3
2394.4.a.p 3
2394.4.a.q 4
2394.4.a.r 4
2394.4.a.s 4
2394.4.a.t 4
2394.4.a.u 4
2394.4.a.v 4
2394.4.a.w 4
2394.4.a.x 4
2394.4.a.y 4
2394.4.a.z 5
2394.4.a.ba 5
2394.4.a.bb 5
2394.4.a.bc 5
2394.4.a.bd 5
2394.4.a.be 6
2394.4.a.bf 6
2394.4.a.bg 7
2394.4.a.bh 7
2394.4.a.bi 7
2394.4.a.bj 7
2394.4.b $$\chi_{2394}(1709, \cdot)$$ n/a 120 1
2394.4.e $$\chi_{2394}(1063, \cdot)$$ n/a 200 1
2394.4.f $$\chi_{2394}(2015, \cdot)$$ n/a 144 1
2394.4.i $$\chi_{2394}(1255, \cdot)$$ n/a 864 2
2394.4.j $$\chi_{2394}(121, \cdot)$$ n/a 960 2
2394.4.k $$\chi_{2394}(799, \cdot)$$ n/a 648 2
2394.4.l $$\chi_{2394}(163, \cdot)$$ n/a 400 2
2394.4.m $$\chi_{2394}(1369, \cdot)$$ n/a 360 2
2394.4.n $$\chi_{2394}(2059, \cdot)$$ n/a 720 2
2394.4.o $$\chi_{2394}(505, \cdot)$$ n/a 300 2
2394.4.p $$\chi_{2394}(961, \cdot)$$ n/a 960 2
2394.4.q $$\chi_{2394}(1075, \cdot)$$ n/a 960 2
2394.4.r $$\chi_{2394}(919, \cdot)$$ n/a 400 2
2394.4.s $$\chi_{2394}(463, \cdot)$$ n/a 720 2
2394.4.t $$\chi_{2394}(1033, \cdot)$$ n/a 960 2
2394.4.u $$\chi_{2394}(457, \cdot)$$ n/a 864 2
2394.4.w $$\chi_{2394}(569, \cdot)$$ n/a 960 2
2394.4.y $$\chi_{2394}(1357, \cdot)$$ n/a 960 2
2394.4.z $$\chi_{2394}(145, \cdot)$$ n/a 400 2
2394.4.bc $$\chi_{2394}(103, \cdot)$$ n/a 960 2
2394.4.bd $$\chi_{2394}(1019, \cdot)$$ n/a 960 2
2394.4.bg $$\chi_{2394}(107, \cdot)$$ n/a 320 2
2394.4.bh $$\chi_{2394}(407, \cdot)$$ n/a 720 2
2394.4.bj $$\chi_{2394}(1291, \cdot)$$ n/a 960 2
2394.4.bl $$\chi_{2394}(425, \cdot)$$ n/a 960 2
2394.4.bo $$\chi_{2394}(125, \cdot)$$ n/a 320 2
2394.4.bp $$\chi_{2394}(311, \cdot)$$ n/a 960 2
2394.4.bx $$\chi_{2394}(83, \cdot)$$ n/a 960 2
2394.4.by $$\chi_{2394}(647, \cdot)$$ n/a 288 2
2394.4.cd $$\chi_{2394}(353, \cdot)$$ n/a 960 2
2394.4.ce $$\chi_{2394}(761, \cdot)$$ n/a 864 2
2394.4.cf $$\chi_{2394}(467, \cdot)$$ n/a 320 2
2394.4.cg $$\chi_{2394}(419, \cdot)$$ n/a 864 2
2394.4.cm $$\chi_{2394}(977, \cdot)$$ n/a 960 2
2394.4.cp $$\chi_{2394}(65, \cdot)$$ n/a 960 2
2394.4.cq $$\chi_{2394}(449, \cdot)$$ n/a 240 2
2394.4.cu $$\chi_{2394}(265, \cdot)$$ n/a 960 2
2394.4.cv $$\chi_{2394}(829, \cdot)$$ n/a 400 2
2394.4.cw $$\chi_{2394}(493, \cdot)$$ n/a 960 2
2394.4.cx $$\chi_{2394}(1741, \cdot)$$ n/a 960 2
2394.4.dc $$\chi_{2394}(1405, \cdot)$$ n/a 400 2
2394.4.dd $$\chi_{2394}(601, \cdot)$$ n/a 960 2
2394.4.de $$\chi_{2394}(2003, \cdot)$$ n/a 720 2
2394.4.df $$\chi_{2394}(683, \cdot)$$ n/a 320 2
2394.4.dk $$\chi_{2394}(863, \cdot)$$ n/a 320 2
2394.4.dl $$\chi_{2394}(113, \cdot)$$ n/a 720 2
2394.4.dm $$\chi_{2394}(905, \cdot)$$ n/a 960 2
2394.4.dn $$\chi_{2394}(2165, \cdot)$$ n/a 960 2
2394.4.dr $$\chi_{2394}(31, \cdot)$$ n/a 960 2
2394.4.ds $$\chi_{2394}(559, \cdot)$$ n/a 400 2
2394.4.dv $$\chi_{2394}(787, \cdot)$$ n/a 960 2
2394.4.dx $$\chi_{2394}(1445, \cdot)$$ n/a 864 2
2394.4.eb $$\chi_{2394}(1109, \cdot)$$ n/a 960 2
2394.4.ee $$\chi_{2394}(1679, \cdot)$$ n/a 960 2
2394.4.ef $$\chi_{2394}(1151, \cdot)$$ n/a 320 2
2394.4.ei $$\chi_{2394}(709, \cdot)$$ n/a 2880 6
2394.4.ej $$\chi_{2394}(25, \cdot)$$ n/a 2880 6
2394.4.ek $$\chi_{2394}(253, \cdot)$$ n/a 900 6
2394.4.el $$\chi_{2394}(43, \cdot)$$ n/a 2160 6
2394.4.em $$\chi_{2394}(289, \cdot)$$ n/a 1200 6
2394.4.en $$\chi_{2394}(823, \cdot)$$ n/a 2880 6
2394.4.eo $$\chi_{2394}(415, \cdot)$$ n/a 1200 6
2394.4.ep $$\chi_{2394}(529, \cdot)$$ n/a 2880 6
2394.4.eq $$\chi_{2394}(841, \cdot)$$ n/a 2160 6
2394.4.er $$\chi_{2394}(29, \cdot)$$ n/a 2160 6
2394.4.es $$\chi_{2394}(1175, \cdot)$$ n/a 2880 6
2394.4.ex $$\chi_{2394}(719, \cdot)$$ n/a 960 6
2394.4.ey $$\chi_{2394}(605, \cdot)$$ n/a 2880 6
2394.4.ez $$\chi_{2394}(515, \cdot)$$ n/a 2880 6
2394.4.fa $$\chi_{2394}(53, \cdot)$$ n/a 960 6
2394.4.fh $$\chi_{2394}(13, \cdot)$$ n/a 2880 6
2394.4.fi $$\chi_{2394}(181, \cdot)$$ n/a 1200 6
2394.4.fj $$\chi_{2394}(535, \cdot)$$ n/a 2880 6
2394.4.fk $$\chi_{2394}(241, \cdot)$$ n/a 2880 6
2394.4.ft $$\chi_{2394}(409, \cdot)$$ n/a 2880 6
2394.4.fu $$\chi_{2394}(325, \cdot)$$ n/a 1200 6
2394.4.fv $$\chi_{2394}(17, \cdot)$$ n/a 960 6
2394.4.fw $$\chi_{2394}(803, \cdot)$$ n/a 2880 6
2394.4.fx $$\chi_{2394}(599, \cdot)$$ n/a 2880 6
2394.4.fy $$\chi_{2394}(485, \cdot)$$ n/a 960 6
2394.4.gh $$\chi_{2394}(155, \cdot)$$ n/a 2160 6
2394.4.gi $$\chi_{2394}(71, \cdot)$$ n/a 720 6
2394.4.gj $$\chi_{2394}(5, \cdot)$$ n/a 2880 6
2394.4.gk $$\chi_{2394}(47, \cdot)$$ n/a 2880 6
2394.4.gl $$\chi_{2394}(401, \cdot)$$ n/a 2880 6
2394.4.gm $$\chi_{2394}(317, \cdot)$$ n/a 2880 6
2394.4.gn $$\chi_{2394}(251, \cdot)$$ n/a 960 6
2394.4.go $$\chi_{2394}(461, \cdot)$$ n/a 2880 6
2394.4.gv $$\chi_{2394}(355, \cdot)$$ n/a 2880 6
2394.4.gw $$\chi_{2394}(649, \cdot)$$ n/a 1200 6
2394.4.hb $$\chi_{2394}(895, \cdot)$$ n/a 2880 6

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(2394))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(2394)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(133))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(171))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(266))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(342))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(399))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(798))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(1197))$$$$^{\oplus 2}$$