Properties

Label 2668.2
Level 2668
Weight 2
Dimension 127430
Nonzero newspaces 24
Sturm bound 887040
Trace bound 9

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Defining parameters

Level: \( N \) = \( 2668 = 2^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(887040\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2668))\).

Total New Old
Modular forms 224840 129694 95146
Cusp forms 218681 127430 91251
Eisenstein series 6159 2264 3895

Trace form

\( 127430 q - 258 q^{2} - 258 q^{4} - 516 q^{5} - 258 q^{6} - 258 q^{8} - 516 q^{9} + O(q^{10}) \) \( 127430 q - 258 q^{2} - 258 q^{4} - 516 q^{5} - 258 q^{6} - 258 q^{8} - 516 q^{9} - 258 q^{10} - 258 q^{12} - 516 q^{13} - 258 q^{14} + 22 q^{15} - 258 q^{16} - 494 q^{17} - 258 q^{18} + 22 q^{19} - 258 q^{20} - 394 q^{21} - 280 q^{22} + 58 q^{23} - 544 q^{24} - 416 q^{25} - 258 q^{26} + 150 q^{27} - 286 q^{28} - 471 q^{29} - 538 q^{30} + 78 q^{31} - 258 q^{32} - 410 q^{33} - 302 q^{34} + 12 q^{35} - 368 q^{36} - 576 q^{37} - 368 q^{38} - 32 q^{39} - 434 q^{40} - 560 q^{41} - 478 q^{42} - 88 q^{43} - 440 q^{44} - 762 q^{45} - 518 q^{46} - 144 q^{47} - 658 q^{48} - 760 q^{49} - 608 q^{50} - 200 q^{51} - 702 q^{52} - 686 q^{53} - 686 q^{54} - 268 q^{55} - 564 q^{56} - 706 q^{57} - 660 q^{58} - 12 q^{59} - 638 q^{60} - 540 q^{61} - 454 q^{62} - 114 q^{63} - 510 q^{64} - 488 q^{65} - 416 q^{66} - 68 q^{67} - 476 q^{68} - 490 q^{69} - 768 q^{70} + 138 q^{71} - 464 q^{72} - 486 q^{73} - 264 q^{74} + 250 q^{75} - 148 q^{76} - 442 q^{77} - 38 q^{78} + 100 q^{79} - 60 q^{80} - 468 q^{81} - 126 q^{82} + 134 q^{83} + 134 q^{84} - 612 q^{85} - 66 q^{86} + 74 q^{87} - 362 q^{88} - 508 q^{89} + 32 q^{90} + 80 q^{91} - 74 q^{92} - 1504 q^{93} - 104 q^{94} + 158 q^{95} + 244 q^{96} - 680 q^{97} + 58 q^{98} + 6 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2668))\)

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
2668.2.a \(\chi_{2668}(1, \cdot)\) 2668.2.a.a 1 1
2668.2.a.b 10
2668.2.a.c 12
2668.2.a.d 13
2668.2.a.e 14
2668.2.c \(\chi_{2668}(1103, \cdot)\) n/a 336 1
2668.2.e \(\chi_{2668}(1565, \cdot)\) 2668.2.e.a 2 1
2668.2.e.b 26
2668.2.e.c 28
2668.2.g \(\chi_{2668}(2667, \cdot)\) n/a 356 1
2668.2.i \(\chi_{2668}(2071, \cdot)\) n/a 660 2
2668.2.k \(\chi_{2668}(505, \cdot)\) n/a 120 2
2668.2.m \(\chi_{2668}(277, \cdot)\) n/a 324 6
2668.2.n \(\chi_{2668}(117, \cdot)\) n/a 560 10
2668.2.p \(\chi_{2668}(91, \cdot)\) n/a 2136 6
2668.2.r \(\chi_{2668}(93, \cdot)\) n/a 336 6
2668.2.t \(\chi_{2668}(459, \cdot)\) n/a 2136 6
2668.2.w \(\chi_{2668}(695, \cdot)\) n/a 3560 10
2668.2.y \(\chi_{2668}(173, \cdot)\) n/a 600 10
2668.2.ba \(\chi_{2668}(175, \cdot)\) n/a 3360 10
2668.2.bd \(\chi_{2668}(137, \cdot)\) n/a 720 12
2668.2.bf \(\chi_{2668}(47, \cdot)\) n/a 3960 12
2668.2.bh \(\chi_{2668}(17, \cdot)\) n/a 1200 20
2668.2.bj \(\chi_{2668}(75, \cdot)\) n/a 7120 20
2668.2.bk \(\chi_{2668}(25, \cdot)\) n/a 3600 60
2668.2.bm \(\chi_{2668}(7, \cdot)\) n/a 21360 60
2668.2.bo \(\chi_{2668}(9, \cdot)\) n/a 3600 60
2668.2.bq \(\chi_{2668}(51, \cdot)\) n/a 21360 60
2668.2.bs \(\chi_{2668}(3, \cdot)\) n/a 42720 120
2668.2.bu \(\chi_{2668}(21, \cdot)\) n/a 7200 120

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2668))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2668)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(667))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1334))\)\(^{\oplus 2}\)