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Properties

Label 1603.2
Level 1603
Weight 2
Dimension 99369
Nonzero newspaces 30
Sturm bound 419520
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1603 = 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(419520\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1603))\).

Total New Old
Modular forms 106248 101641 4607
Cusp forms 103513 99369 4144
Eisenstein series 2735 2272 463

Trace form

\( 99369 q - 459 q^{2} - 460 q^{3} - 463 q^{4} - 462 q^{5} - 468 q^{6} - 571 q^{7} - 1155 q^{8} - 469 q^{9} + O(q^{10}) \) \( 99369 q - 459 q^{2} - 460 q^{3} - 463 q^{4} - 462 q^{5} - 468 q^{6} - 571 q^{7} - 1155 q^{8} - 469 q^{9} - 474 q^{10} - 468 q^{11} - 484 q^{12} - 470 q^{13} - 573 q^{14} - 1164 q^{15} - 487 q^{16} - 474 q^{17} - 495 q^{18} - 476 q^{19} - 498 q^{20} - 574 q^{21} - 1176 q^{22} - 480 q^{23} - 516 q^{24} - 487 q^{25} - 498 q^{26} - 496 q^{27} - 577 q^{28} - 1170 q^{29} - 528 q^{30} - 488 q^{31} - 519 q^{32} - 504 q^{33} - 510 q^{34} - 576 q^{35} - 1231 q^{36} - 494 q^{37} - 516 q^{38} - 512 q^{39} - 546 q^{40} - 498 q^{41} - 582 q^{42} - 1184 q^{43} - 540 q^{44} - 534 q^{45} - 528 q^{46} - 504 q^{47} - 580 q^{48} - 571 q^{49} - 1233 q^{50} - 528 q^{51} - 554 q^{52} - 510 q^{53} - 576 q^{54} - 528 q^{55} - 585 q^{56} - 1220 q^{57} - 546 q^{58} - 516 q^{59} - 624 q^{60} - 518 q^{61} - 552 q^{62} - 583 q^{63} - 1267 q^{64} - 540 q^{65} - 600 q^{66} - 524 q^{67} - 582 q^{68} - 552 q^{69} - 588 q^{70} - 1212 q^{71} - 651 q^{72} - 530 q^{73} - 570 q^{74} - 580 q^{75} - 596 q^{76} - 582 q^{77} - 1308 q^{78} - 536 q^{79} - 642 q^{80} - 577 q^{81} - 582 q^{82} - 540 q^{83} - 598 q^{84} - 1248 q^{85} - 588 q^{86} - 576 q^{87} - 636 q^{88} - 546 q^{89} - 690 q^{90} - 584 q^{91} - 1308 q^{92} - 584 q^{93} - 600 q^{94} - 576 q^{95} - 708 q^{96} - 554 q^{97} - 573 q^{98} - 1296 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1603))\)

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
1603.2.a \(\chi_{1603}(1, \cdot)\) 1603.2.a.a 3 1
1603.2.a.b 23
1603.2.a.c 26
1603.2.a.d 31
1603.2.a.e 32
1603.2.c \(\chi_{1603}(1373, \cdot)\) n/a 114 1
1603.2.e \(\chi_{1603}(781, \cdot)\) n/a 302 2
1603.2.f \(\chi_{1603}(459, \cdot)\) n/a 304 2
1603.2.g \(\chi_{1603}(592, \cdot)\) n/a 302 2
1603.2.h \(\chi_{1603}(134, \cdot)\) n/a 232 2
1603.2.i \(\chi_{1603}(580, \cdot)\) n/a 300 2
1603.2.k \(\chi_{1603}(1051, \cdot)\) n/a 228 2
1603.2.q \(\chi_{1603}(228, \cdot)\) n/a 304 2
1603.2.r \(\chi_{1603}(324, \cdot)\) n/a 302 2
1603.2.u \(\chi_{1603}(95, \cdot)\) n/a 302 2
1603.2.w \(\chi_{1603}(318, \cdot)\) n/a 604 4
1603.2.ba \(\chi_{1603}(440, \cdot)\) n/a 608 4
1603.2.bb \(\chi_{1603}(122, \cdot)\) n/a 608 4
1603.2.bc \(\chi_{1603}(89, \cdot)\) n/a 604 4
1603.2.be \(\chi_{1603}(43, \cdot)\) n/a 2088 18
1603.2.bg \(\chi_{1603}(15, \cdot)\) n/a 2052 18
1603.2.bi \(\chi_{1603}(183, \cdot)\) n/a 4176 36
1603.2.bj \(\chi_{1603}(9, \cdot)\) n/a 5436 36
1603.2.bk \(\chi_{1603}(16, \cdot)\) n/a 5472 36
1603.2.bl \(\chi_{1603}(37, \cdot)\) n/a 5436 36
1603.2.bn \(\chi_{1603}(13, \cdot)\) n/a 5400 36
1603.2.bp \(\chi_{1603}(46, \cdot)\) n/a 5436 36
1603.2.bs \(\chi_{1603}(58, \cdot)\) n/a 5436 36
1603.2.bt \(\chi_{1603}(4, \cdot)\) n/a 5472 36
1603.2.bz \(\chi_{1603}(36, \cdot)\) n/a 4104 36
1603.2.cb \(\chi_{1603}(10, \cdot)\) n/a 10872 72
1603.2.cc \(\chi_{1603}(52, \cdot)\) n/a 10944 72
1603.2.cd \(\chi_{1603}(6, \cdot)\) n/a 10944 72
1603.2.ch \(\chi_{1603}(24, \cdot)\) n/a 10872 72

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1603))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1603)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(229))\)\(^{\oplus 2}\)