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Properties

Label 1003.6.l
Level $1003$
Weight $6$
Character orbit 1003.l
Rep. character $\chi_{1003}(16,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $12544$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 1003 = 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1003.l (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1003 \)
Character field: \(\Q(\zeta_{58})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1003, [\chi])\).

Total New Old
Modular forms 12656 12656 0
Cusp forms 12544 12544 0
Eisenstein series 112 112 0

Trace form

\( 12544 q - 62 q^{2} - 7190 q^{4} - 310 q^{8} + 35778 q^{9} + O(q^{10}) \) \( 12544 q - 62 q^{2} - 7190 q^{4} - 310 q^{8} + 35778 q^{9} + 218 q^{13} + 60 q^{15} - 111558 q^{16} + 1862 q^{17} + 5210 q^{18} - 2126 q^{19} - 8628 q^{21} + 274946 q^{25} - 23826 q^{26} - 726 q^{30} - 21366 q^{32} - 14230 q^{33} + 4677 q^{34} + 4528 q^{35} + 565918 q^{36} + 36666 q^{38} - 46646 q^{42} + 6118 q^{43} + 95788 q^{47} + 822494 q^{49} + 214422 q^{50} - 239717 q^{51} + 403946 q^{52} - 63808 q^{53} + 38070 q^{55} - 96214 q^{59} - 2133164 q^{60} - 2371358 q^{64} - 1441194 q^{66} + 55372 q^{67} - 554007 q^{68} + 1450566 q^{69} - 943846 q^{70} + 268030 q^{72} - 329302 q^{76} - 396234 q^{77} - 2876138 q^{81} - 336462 q^{83} - 491786 q^{84} + 39203 q^{85} + 512722 q^{86} - 76300 q^{87} - 104066 q^{89} - 703630 q^{93} - 626002 q^{94} + 513446 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(1003, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.