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Properties

Label 1003.2
Level 1003
Weight 2
Dimension 40589
Nonzero newspaces 10
Sturm bound 167040
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1003 = 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(167040\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1003))\).

Total New Old
Modular forms 42688 42301 387
Cusp forms 40833 40589 244
Eisenstein series 1855 1712 143

Trace form

\( 40589 q - 399 q^{2} - 402 q^{3} - 411 q^{4} - 408 q^{5} - 426 q^{6} - 414 q^{7} - 435 q^{8} - 429 q^{9} + O(q^{10}) \) \( 40589 q - 399 q^{2} - 402 q^{3} - 411 q^{4} - 408 q^{5} - 426 q^{6} - 414 q^{7} - 435 q^{8} - 429 q^{9} - 436 q^{10} - 410 q^{11} - 426 q^{12} - 416 q^{13} - 430 q^{14} - 414 q^{15} - 411 q^{16} - 438 q^{17} - 891 q^{18} - 434 q^{19} - 460 q^{20} - 438 q^{21} - 466 q^{22} - 446 q^{23} - 490 q^{24} - 427 q^{25} - 444 q^{26} - 462 q^{27} - 462 q^{28} - 440 q^{29} - 478 q^{30} - 422 q^{31} - 467 q^{32} - 454 q^{33} - 396 q^{34} - 918 q^{35} - 503 q^{36} - 440 q^{37} - 474 q^{38} - 462 q^{39} - 468 q^{40} - 428 q^{41} - 486 q^{42} - 442 q^{43} - 450 q^{44} - 462 q^{45} - 394 q^{46} - 396 q^{47} - 206 q^{48} - 381 q^{49} - 309 q^{50} - 379 q^{51} - 772 q^{52} - 348 q^{53} - 104 q^{54} - 304 q^{55} - 46 q^{56} - 148 q^{57} - 310 q^{58} - 337 q^{59} - 268 q^{60} - 332 q^{61} - 354 q^{62} - 172 q^{63} - 83 q^{64} - 316 q^{65} - 160 q^{66} - 398 q^{67} - 348 q^{68} - 670 q^{69} - 318 q^{70} - 394 q^{71} - 235 q^{72} - 354 q^{73} - 448 q^{74} - 448 q^{75} - 570 q^{76} - 518 q^{77} - 558 q^{78} - 502 q^{79} - 596 q^{80} - 545 q^{81} - 552 q^{82} - 514 q^{83} - 694 q^{84} - 445 q^{85} - 1010 q^{86} - 558 q^{87} - 610 q^{88} - 516 q^{89} - 636 q^{90} - 502 q^{91} - 510 q^{92} - 582 q^{93} - 502 q^{94} - 526 q^{95} - 618 q^{96} - 556 q^{97} - 385 q^{98} - 380 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1003))\)

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
1003.2.a \(\chi_{1003}(1, \cdot)\) 1003.2.a.a 1 1
1003.2.a.b 1
1003.2.a.c 1
1003.2.a.d 1
1003.2.a.e 3
1003.2.a.f 4
1003.2.a.g 10
1003.2.a.h 16
1003.2.a.i 18
1003.2.a.j 22
1003.2.d \(\chi_{1003}(237, \cdot)\) 1003.2.d.a 2 1
1003.2.d.b 4
1003.2.d.c 38
1003.2.d.d 44
1003.2.e \(\chi_{1003}(591, \cdot)\) n/a 176 2
1003.2.g \(\chi_{1003}(60, \cdot)\) n/a 344 4
1003.2.i \(\chi_{1003}(58, \cdot)\) n/a 704 8
1003.2.k \(\chi_{1003}(35, \cdot)\) n/a 2240 28
1003.2.l \(\chi_{1003}(16, \cdot)\) n/a 2464 28
1003.2.p \(\chi_{1003}(4, \cdot)\) n/a 4928 56
1003.2.r \(\chi_{1003}(9, \cdot)\) n/a 9856 112
1003.2.t \(\chi_{1003}(6, \cdot)\) n/a 19712 224

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1003))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1003)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)