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Properties

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

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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

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

Display 100 coefficients 10 coefficients

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

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