↑

Properties

Label 1007.2
Level 1007
Weight 2
Dimension 40987
Nonzero newspaces 18
Sturm bound 168480
Trace bound 4

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 1007 = 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(168480\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1007))\).

Total New Old
Modular forms 43056 42723 333
Cusp forms 41185 40987 198
Eisenstein series 1871 1736 135

Trace form

\( 40987 q - 407 q^{2} - 410 q^{3} - 419 q^{4} - 416 q^{5} - 434 q^{6} - 422 q^{7} - 443 q^{8} - 437 q^{9} + O(q^{10}) \) \( 40987 q - 407 q^{2} - 410 q^{3} - 419 q^{4} - 416 q^{5} - 434 q^{6} - 422 q^{7} - 443 q^{8} - 437 q^{9} - 452 q^{10} - 434 q^{11} - 458 q^{12} - 416 q^{13} - 434 q^{14} - 434 q^{15} - 419 q^{16} - 434 q^{17} - 443 q^{18} - 421 q^{19} - 902 q^{20} - 452 q^{21} - 452 q^{22} - 452 q^{23} - 506 q^{24} - 455 q^{25} - 488 q^{26} - 476 q^{27} - 488 q^{28} - 452 q^{29} - 488 q^{30} - 458 q^{31} - 497 q^{32} - 434 q^{33} - 470 q^{34} - 470 q^{35} - 455 q^{36} - 458 q^{37} - 415 q^{38} - 908 q^{39} - 428 q^{40} - 436 q^{41} - 298 q^{42} - 348 q^{43} - 298 q^{44} - 210 q^{45} - 348 q^{46} - 400 q^{47} + 2 q^{48} - 387 q^{49} - 245 q^{50} - 298 q^{51} - 196 q^{52} - 322 q^{53} - 700 q^{54} - 386 q^{55} - 212 q^{56} - 386 q^{57} - 812 q^{58} - 384 q^{59} - 76 q^{60} - 400 q^{61} - 384 q^{62} - 282 q^{63} - 295 q^{64} - 348 q^{65} - 334 q^{66} - 364 q^{67} - 446 q^{68} - 488 q^{69} - 542 q^{70} - 488 q^{71} - 587 q^{72} - 452 q^{73} - 560 q^{74} - 584 q^{75} - 517 q^{76} - 938 q^{77} - 614 q^{78} - 434 q^{79} - 632 q^{80} - 527 q^{81} - 434 q^{82} - 524 q^{83} - 638 q^{84} - 506 q^{85} - 596 q^{86} - 366 q^{87} - 354 q^{88} - 376 q^{89} - 270 q^{90} - 358 q^{91} - 200 q^{92} - 370 q^{93} + 28 q^{94} - 428 q^{95} - 652 q^{96} - 124 q^{97} - 153 q^{98} - 76 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1007))\)

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
1007.2.a \(\chi_{1007}(1, \cdot)\) 1007.2.a.a 1 1
1007.2.a.b 12
1007.2.a.c 12
1007.2.a.d 26
1007.2.a.e 28
1007.2.b \(\chi_{1007}(476, \cdot)\) 1007.2.b.a 80 1
1007.2.e \(\chi_{1007}(372, \cdot)\) n/a 176 2
1007.2.f \(\chi_{1007}(189, \cdot)\) n/a 176 2
1007.2.j \(\chi_{1007}(847, \cdot)\) n/a 176 2
1007.2.k \(\chi_{1007}(54, \cdot)\) n/a 516 6
1007.2.m \(\chi_{1007}(772, \cdot)\) n/a 352 4
1007.2.n \(\chi_{1007}(77, \cdot)\) n/a 984 12
1007.2.p \(\chi_{1007}(158, \cdot)\) n/a 528 6
1007.2.t \(\chi_{1007}(96, \cdot)\) n/a 960 12
1007.2.v \(\chi_{1007}(129, \cdot)\) n/a 1056 12
1007.2.w \(\chi_{1007}(49, \cdot)\) n/a 2112 24
1007.2.y \(\chi_{1007}(18, \cdot)\) n/a 2112 24
1007.2.z \(\chi_{1007}(7, \cdot)\) n/a 2112 24
1007.2.bc \(\chi_{1007}(16, \cdot)\) n/a 6336 72
1007.2.bd \(\chi_{1007}(8, \cdot)\) n/a 4224 48
1007.2.bg \(\chi_{1007}(4, \cdot)\) n/a 6336 72
1007.2.bi \(\chi_{1007}(2, \cdot)\) n/a 12672 144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1007))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1007)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 2}\)