Properties

Label 2667.2
Level 2667
Weight 2
Dimension 184203
Nonzero newspaces 64
Sturm bound 1032192
Trace bound 8

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Defining parameters

Level: \( N \) = \( 2667 = 3 \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(1032192\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2667))\).

Total New Old
Modular forms 261072 186699 74373
Cusp forms 255025 184203 70822
Eisenstein series 6047 2496 3551

Trace form

\( 184203 q + 9 q^{2} - 245 q^{3} - 487 q^{4} + 6 q^{5} - 255 q^{6} - 619 q^{7} + 9 q^{8} - 257 q^{9} + O(q^{10}) \) \( 184203 q + 9 q^{2} - 245 q^{3} - 487 q^{4} + 6 q^{5} - 255 q^{6} - 619 q^{7} + 9 q^{8} - 257 q^{9} - 498 q^{10} - 251 q^{12} - 490 q^{13} - 3 q^{14} - 612 q^{15} - 471 q^{16} + 30 q^{17} - 243 q^{18} - 472 q^{19} + 54 q^{20} - 308 q^{21} - 1200 q^{22} + 24 q^{23} - 243 q^{24} - 483 q^{25} + 42 q^{26} - 257 q^{27} - 657 q^{28} + 18 q^{29} - 246 q^{30} - 484 q^{31} + 57 q^{32} - 252 q^{33} - 462 q^{34} + 6 q^{35} - 605 q^{36} - 470 q^{37} + 72 q^{38} - 238 q^{39} - 402 q^{40} + 78 q^{41} - 294 q^{42} - 1208 q^{43} + 84 q^{44} - 246 q^{45} - 432 q^{46} + 36 q^{47} - 203 q^{48} - 627 q^{49} + 99 q^{50} - 222 q^{51} - 394 q^{52} + 66 q^{53} - 243 q^{54} - 432 q^{55} + 21 q^{56} - 658 q^{57} - 402 q^{58} + 12 q^{59} - 222 q^{60} - 442 q^{61} + 24 q^{62} - 344 q^{63} - 1147 q^{64} + 72 q^{65} - 216 q^{66} - 432 q^{67} + 114 q^{68} - 228 q^{69} - 576 q^{70} + 96 q^{71} - 243 q^{72} - 370 q^{73} + 138 q^{74} - 191 q^{75} - 364 q^{76} + 36 q^{77} - 600 q^{78} - 420 q^{79} + 198 q^{80} - 233 q^{81} - 414 q^{82} + 84 q^{83} - 302 q^{84} - 1176 q^{85} + 144 q^{86} - 210 q^{87} - 348 q^{88} + 150 q^{89} - 222 q^{90} - 628 q^{91} + 168 q^{92} - 172 q^{93} - 384 q^{94} + 132 q^{95} - 195 q^{96} - 418 q^{97} - 3 q^{98} - 618 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2667))\)

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
2667.2.a \(\chi_{2667}(1, \cdot)\) 2667.2.a.a 1 1
2667.2.a.b 1
2667.2.a.c 1
2667.2.a.d 1
2667.2.a.e 1
2667.2.a.f 2
2667.2.a.g 2
2667.2.a.h 2
2667.2.a.i 2
2667.2.a.j 7
2667.2.a.k 11
2667.2.a.l 13
2667.2.a.m 14
2667.2.a.n 16
2667.2.a.o 16
2667.2.a.p 18
2667.2.a.q 19
2667.2.d \(\chi_{2667}(2414, \cdot)\) n/a 336 1
2667.2.e \(\chi_{2667}(1142, \cdot)\) n/a 256 1
2667.2.h \(\chi_{2667}(1777, \cdot)\) n/a 172 1
2667.2.i \(\chi_{2667}(361, \cdot)\) n/a 340 2
2667.2.j \(\chi_{2667}(382, \cdot)\) n/a 336 2
2667.2.k \(\chi_{2667}(781, \cdot)\) n/a 340 2
2667.2.l \(\chi_{2667}(400, \cdot)\) n/a 256 2
2667.2.o \(\chi_{2667}(743, \cdot)\) n/a 512 2
2667.2.p \(\chi_{2667}(146, \cdot)\) n/a 672 2
2667.2.q \(\chi_{2667}(1396, \cdot)\) n/a 340 2
2667.2.r \(\chi_{2667}(1417, \cdot)\) n/a 340 2
2667.2.s \(\chi_{2667}(997, \cdot)\) n/a 340 2
2667.2.z \(\chi_{2667}(401, \cdot)\) n/a 676 2
2667.2.ba \(\chi_{2667}(488, \cdot)\) n/a 676 2
2667.2.bb \(\chi_{2667}(509, \cdot)\) n/a 672 2
2667.2.bc \(\chi_{2667}(1544, \cdot)\) n/a 676 2
2667.2.bd \(\chi_{2667}(908, \cdot)\) n/a 676 2
2667.2.be \(\chi_{2667}(380, \cdot)\) n/a 676 2
2667.2.bn \(\chi_{2667}(1378, \cdot)\) n/a 344 2
2667.2.bo \(\chi_{2667}(64, \cdot)\) n/a 768 6
2667.2.bp \(\chi_{2667}(37, \cdot)\) n/a 1026 6
2667.2.bq \(\chi_{2667}(226, \cdot)\) n/a 1026 6
2667.2.br \(\chi_{2667}(22, \cdot)\) n/a 768 6
2667.2.bs \(\chi_{2667}(349, \cdot)\) n/a 1032 6
2667.2.bv \(\chi_{2667}(365, \cdot)\) n/a 1536 6
2667.2.bw \(\chi_{2667}(524, \cdot)\) n/a 2016 6
2667.2.bz \(\chi_{2667}(155, \cdot)\) n/a 1536 6
2667.2.ca \(\chi_{2667}(230, \cdot)\) n/a 2028 6
2667.2.cf \(\chi_{2667}(313, \cdot)\) n/a 1026 6
2667.2.ci \(\chi_{2667}(598, \cdot)\) n/a 1026 6
2667.2.cl \(\chi_{2667}(68, \cdot)\) n/a 2022 6
2667.2.cm \(\chi_{2667}(359, \cdot)\) n/a 2022 6
2667.2.cp \(\chi_{2667}(725, \cdot)\) n/a 2022 6
2667.2.cq \(\chi_{2667}(164, \cdot)\) n/a 2022 6
2667.2.cr \(\chi_{2667}(202, \cdot)\) n/a 1020 6
2667.2.cu \(\chi_{2667}(442, \cdot)\) n/a 1536 12
2667.2.cv \(\chi_{2667}(25, \cdot)\) n/a 2040 12
2667.2.cw \(\chi_{2667}(4, \cdot)\) n/a 2040 12
2667.2.cx \(\chi_{2667}(100, \cdot)\) n/a 2040 12
2667.2.cy \(\chi_{2667}(160, \cdot)\) n/a 2064 12
2667.2.dh \(\chi_{2667}(95, \cdot)\) n/a 4056 12
2667.2.di \(\chi_{2667}(122, \cdot)\) n/a 4056 12
2667.2.dj \(\chi_{2667}(137, \cdot)\) n/a 4056 12
2667.2.dk \(\chi_{2667}(131, \cdot)\) n/a 4056 12
2667.2.dl \(\chi_{2667}(38, \cdot)\) n/a 4056 12
2667.2.dm \(\chi_{2667}(305, \cdot)\) n/a 4056 12
2667.2.dt \(\chi_{2667}(40, \cdot)\) n/a 2040 12
2667.2.du \(\chi_{2667}(10, \cdot)\) n/a 2040 12
2667.2.dv \(\chi_{2667}(250, \cdot)\) n/a 2040 12
2667.2.dw \(\chi_{2667}(188, \cdot)\) n/a 4032 12
2667.2.dx \(\chi_{2667}(281, \cdot)\) n/a 3072 12
2667.2.ea \(\chi_{2667}(148, \cdot)\) n/a 4608 36
2667.2.eb \(\chi_{2667}(79, \cdot)\) n/a 6156 36
2667.2.ec \(\chi_{2667}(163, \cdot)\) n/a 6156 36
2667.2.ef \(\chi_{2667}(55, \cdot)\) n/a 6120 36
2667.2.eg \(\chi_{2667}(23, \cdot)\) n/a 12132 36
2667.2.eh \(\chi_{2667}(17, \cdot)\) n/a 12132 36
2667.2.ek \(\chi_{2667}(206, \cdot)\) n/a 12132 36
2667.2.el \(\chi_{2667}(86, \cdot)\) n/a 12132 36
2667.2.eo \(\chi_{2667}(220, \cdot)\) n/a 6156 36
2667.2.er \(\chi_{2667}(166, \cdot)\) n/a 6156 36
2667.2.ew \(\chi_{2667}(29, \cdot)\) n/a 9216 36
2667.2.ex \(\chi_{2667}(41, \cdot)\) n/a 12168 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2667))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2667)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(127))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(381))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(889))\)\(^{\oplus 2}\)