Properties

 Label 2368.2 Level 2368 Weight 2 Dimension 97582 Nonzero newspaces 42 Sturm bound 700416 Trace bound 43

Defining parameters

 Level: $$N$$ = $$2368 = 2^{6} \cdot 37$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$42$$ Sturm bound: $$700416$$ Trace bound: $$43$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2368))$$.

Total New Old
Modular forms 177696 99122 78574
Cusp forms 172513 97582 74931
Eisenstein series 5183 1540 3643

Trace form

 $$97582 q - 272 q^{2} - 204 q^{3} - 272 q^{4} - 272 q^{5} - 272 q^{6} - 200 q^{7} - 272 q^{8} - 334 q^{9} + O(q^{10})$$ $$97582 q - 272 q^{2} - 204 q^{3} - 272 q^{4} - 272 q^{5} - 272 q^{6} - 200 q^{7} - 272 q^{8} - 334 q^{9} - 272 q^{10} - 196 q^{11} - 272 q^{12} - 256 q^{13} - 272 q^{14} - 192 q^{15} - 272 q^{16} - 460 q^{17} - 272 q^{18} - 188 q^{19} - 272 q^{20} - 280 q^{21} - 288 q^{22} - 200 q^{23} - 352 q^{24} - 362 q^{25} - 352 q^{26} - 216 q^{27} - 352 q^{28} - 304 q^{29} - 432 q^{30} - 248 q^{31} - 352 q^{32} - 256 q^{33} - 352 q^{34} - 208 q^{35} - 432 q^{36} - 288 q^{37} - 640 q^{38} - 200 q^{39} - 352 q^{40} - 340 q^{41} - 352 q^{42} - 180 q^{43} - 288 q^{44} - 264 q^{45} - 272 q^{46} - 168 q^{47} - 272 q^{48} - 458 q^{49} - 224 q^{50} - 256 q^{51} - 176 q^{52} - 224 q^{53} - 144 q^{54} - 328 q^{55} - 160 q^{56} - 328 q^{57} - 128 q^{58} - 340 q^{59} - 80 q^{60} - 256 q^{61} - 208 q^{62} - 336 q^{63} - 80 q^{64} - 744 q^{65} - 112 q^{66} - 380 q^{67} - 176 q^{68} - 248 q^{69} - 80 q^{70} - 328 q^{71} - 128 q^{72} - 340 q^{73} - 224 q^{74} - 532 q^{75} - 144 q^{76} - 280 q^{77} - 224 q^{78} - 264 q^{79} - 352 q^{80} - 482 q^{81} - 432 q^{82} - 204 q^{83} - 496 q^{84} - 288 q^{85} - 480 q^{86} - 200 q^{87} - 432 q^{88} - 436 q^{89} - 560 q^{90} - 192 q^{91} - 576 q^{92} - 352 q^{93} - 464 q^{94} - 240 q^{95} - 544 q^{96} - 284 q^{97} - 544 q^{98} - 252 q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2368))$$

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
2368.2.a $$\chi_{2368}(1, \cdot)$$ 2368.2.a.a 1 1
2368.2.a.b 1
2368.2.a.c 1
2368.2.a.d 1
2368.2.a.e 1
2368.2.a.f 1
2368.2.a.g 1
2368.2.a.h 1
2368.2.a.i 1
2368.2.a.j 1
2368.2.a.k 1
2368.2.a.l 1
2368.2.a.m 1
2368.2.a.n 1
2368.2.a.o 1
2368.2.a.p 1
2368.2.a.q 1
2368.2.a.r 1
2368.2.a.s 2
2368.2.a.t 2
2368.2.a.u 2
2368.2.a.v 2
2368.2.a.w 2
2368.2.a.x 2
2368.2.a.y 2
2368.2.a.z 2
2368.2.a.ba 2
2368.2.a.bb 3
2368.2.a.bc 3
2368.2.a.bd 3
2368.2.a.be 3
2368.2.a.bf 4
2368.2.a.bg 4
2368.2.a.bh 4
2368.2.a.bi 4
2368.2.a.bj 8
2368.2.c $$\chi_{2368}(1185, \cdot)$$ 2368.2.c.a 12 1
2368.2.c.b 12
2368.2.c.c 24
2368.2.c.d 24
2368.2.e $$\chi_{2368}(2145, \cdot)$$ 2368.2.e.a 8 1
2368.2.e.b 20
2368.2.e.c 48
2368.2.g $$\chi_{2368}(961, \cdot)$$ 2368.2.g.a 2 1
2368.2.g.b 2
2368.2.g.c 2
2368.2.g.d 2
2368.2.g.e 2
2368.2.g.f 2
2368.2.g.g 2
2368.2.g.h 4
2368.2.g.i 4
2368.2.g.j 4
2368.2.g.k 6
2368.2.g.l 6
2368.2.g.m 8
2368.2.g.n 8
2368.2.g.o 10
2368.2.g.p 10
2368.2.i $$\chi_{2368}(1025, \cdot)$$ n/a 148 2
2368.2.j $$\chi_{2368}(31, \cdot)$$ n/a 152 2
2368.2.m $$\chi_{2368}(623, \cdot)$$ n/a 148 2
2368.2.n $$\chi_{2368}(369, \cdot)$$ n/a 148 2
2368.2.o $$\chi_{2368}(593, \cdot)$$ n/a 144 2
2368.2.s $$\chi_{2368}(1807, \cdot)$$ n/a 148 2
2368.2.t $$\chi_{2368}(191, \cdot)$$ n/a 148 2
2368.2.w $$\chi_{2368}(1729, \cdot)$$ n/a 148 2
2368.2.y $$\chi_{2368}(545, \cdot)$$ n/a 152 2
2368.2.ba $$\chi_{2368}(417, \cdot)$$ n/a 152 2
2368.2.bc $$\chi_{2368}(297, \cdot)$$ None 0 4
2368.2.bf $$\chi_{2368}(487, \cdot)$$ None 0 4
2368.2.bh $$\chi_{2368}(327, \cdot)$$ None 0 4
2368.2.bj $$\chi_{2368}(73, \cdot)$$ None 0 4
2368.2.bk $$\chi_{2368}(641, \cdot)$$ n/a 444 6
2368.2.bm $$\chi_{2368}(319, \cdot)$$ n/a 296 4
2368.2.bn $$\chi_{2368}(399, \cdot)$$ n/a 296 4
2368.2.br $$\chi_{2368}(433, \cdot)$$ n/a 296 4
2368.2.bs $$\chi_{2368}(529, \cdot)$$ n/a 296 4
2368.2.bt $$\chi_{2368}(495, \cdot)$$ n/a 296 4
2368.2.bw $$\chi_{2368}(415, \cdot)$$ n/a 304 4
2368.2.by $$\chi_{2368}(43, \cdot)$$ n/a 2416 8
2368.2.ca $$\chi_{2368}(149, \cdot)$$ n/a 2304 8
2368.2.cc $$\chi_{2368}(221, \cdot)$$ n/a 2416 8
2368.2.cd $$\chi_{2368}(339, \cdot)$$ n/a 2416 8
2368.2.cg $$\chi_{2368}(65, \cdot)$$ n/a 444 6
2368.2.ci $$\chi_{2368}(33, \cdot)$$ n/a 456 6
2368.2.cl $$\chi_{2368}(225, \cdot)$$ n/a 456 6
2368.2.cm $$\chi_{2368}(233, \cdot)$$ None 0 8
2368.2.cp $$\chi_{2368}(615, \cdot)$$ None 0 8
2368.2.cr $$\chi_{2368}(23, \cdot)$$ None 0 8
2368.2.ct $$\chi_{2368}(121, \cdot)$$ None 0 8
2368.2.cv $$\chi_{2368}(383, \cdot)$$ n/a 888 12
2368.2.cw $$\chi_{2368}(337, \cdot)$$ n/a 888 12
2368.2.cy $$\chi_{2368}(15, \cdot)$$ n/a 888 12
2368.2.db $$\chi_{2368}(79, \cdot)$$ n/a 888 12
2368.2.dc $$\chi_{2368}(49, \cdot)$$ n/a 888 12
2368.2.df $$\chi_{2368}(351, \cdot)$$ n/a 912 12
2368.2.dh $$\chi_{2368}(251, \cdot)$$ n/a 4832 16
2368.2.dj $$\chi_{2368}(269, \cdot)$$ n/a 4832 16
2368.2.dl $$\chi_{2368}(85, \cdot)$$ n/a 4832 16
2368.2.dm $$\chi_{2368}(51, \cdot)$$ n/a 4832 16
2368.2.do $$\chi_{2368}(39, \cdot)$$ None 0 24
2368.2.dr $$\chi_{2368}(25, \cdot)$$ None 0 24
2368.2.dt $$\chi_{2368}(9, \cdot)$$ None 0 24
2368.2.du $$\chi_{2368}(55, \cdot)$$ None 0 24
2368.2.dw $$\chi_{2368}(53, \cdot)$$ n/a 14496 48
2368.2.ea $$\chi_{2368}(59, \cdot)$$ n/a 14496 48
2368.2.eb $$\chi_{2368}(19, \cdot)$$ n/a 14496 48
2368.2.ec $$\chi_{2368}(21, \cdot)$$ n/a 14496 48

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2368))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2368)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(37))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(74))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(148))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(296))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(592))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1184))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2368))$$$$^{\oplus 1}$$