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Properties

Label 1003.6
Level 1003
Weight 6
Dimension 206376
Nonzero newspaces 10
Sturm bound 501120
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1003 = 17 \cdot 59 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(501120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(1003))\).

Total New Old
Modular forms 209728 208088 1640
Cusp forms 207872 206376 1496
Eisenstein series 1856 1712 144

Trace form

\( 206376 q - 390 q^{2} - 390 q^{3} - 390 q^{4} - 390 q^{5} - 390 q^{6} - 390 q^{7} - 390 q^{8} - 390 q^{9} + O(q^{10}) \) \( 206376 q - 390 q^{2} - 390 q^{3} - 390 q^{4} - 390 q^{5} - 390 q^{6} - 390 q^{7} - 390 q^{8} - 390 q^{9} + 2138 q^{10} - 1654 q^{11} - 8838 q^{12} - 2006 q^{13} + 1018 q^{14} + 8298 q^{15} + 13962 q^{16} + 3405 q^{17} + 7098 q^{18} - 1526 q^{19} - 17414 q^{20} - 24822 q^{21} - 19462 q^{22} - 7606 q^{23} + 44442 q^{24} + 14226 q^{25} - 25062 q^{26} - 43158 q^{27} - 66726 q^{28} - 12190 q^{29} + 21498 q^{30} + 38330 q^{31} + 74442 q^{32} + 69322 q^{33} + 134621 q^{34} + 51706 q^{35} + 51962 q^{36} - 10054 q^{37} + 29354 q^{38} - 25510 q^{39} - 266502 q^{40} - 166798 q^{41} - 392550 q^{42} - 117110 q^{43} - 156230 q^{44} + 536768 q^{45} + 591146 q^{46} + 69052 q^{47} - 446870 q^{48} - 197690 q^{49} - 417302 q^{50} - 133103 q^{51} - 107462 q^{52} + 271694 q^{53} + 631858 q^{54} + 251328 q^{55} + 687690 q^{56} + 242888 q^{57} - 312300 q^{58} + 125510 q^{59} + 865268 q^{60} - 22218 q^{61} - 101862 q^{62} + 220484 q^{63} - 141862 q^{64} + 256484 q^{65} - 540862 q^{66} - 319874 q^{67} + 538125 q^{68} - 270318 q^{69} - 386006 q^{70} - 233954 q^{71} - 81142 q^{72} - 286408 q^{73} + 872266 q^{74} + 113764 q^{75} - 1291222 q^{76} - 880102 q^{77} - 1712534 q^{78} - 397830 q^{79} - 126918 q^{80} + 130378 q^{81} + 942346 q^{82} + 1372986 q^{83} + 4194218 q^{84} + 1857525 q^{85} + 402842 q^{86} + 12090 q^{87} - 339206 q^{88} - 850518 q^{89} - 2377414 q^{90} - 1413542 q^{91} - 2459174 q^{92} - 1127494 q^{93} - 1694534 q^{94} - 683046 q^{95} - 547670 q^{96} - 397190 q^{97} + 7102364 q^{98} + 5014640 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(1003))\)

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
1003.6.a \(\chi_{1003}(1, \cdot)\) 1003.6.a.a 94 1
1003.6.a.b 96
1003.6.a.c 98
1003.6.a.d 100
1003.6.d \(\chi_{1003}(237, \cdot)\) n/a 436 1
1003.6.e \(\chi_{1003}(591, \cdot)\) n/a 872 2
1003.6.g \(\chi_{1003}(60, \cdot)\) n/a 1736 4
1003.6.i \(\chi_{1003}(58, \cdot)\) n/a 3584 8
1003.6.k \(\chi_{1003}(35, \cdot)\) n/a 11200 28
1003.6.l \(\chi_{1003}(16, \cdot)\) n/a 12544 28
1003.6.p \(\chi_{1003}(4, \cdot)\) n/a 25088 56
1003.6.r \(\chi_{1003}(9, \cdot)\) n/a 50176 112
1003.6.t \(\chi_{1003}(6, \cdot)\) n/a 100352 224

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(1003))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(1003)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(1003))\)\(^{\oplus 1}\)