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Properties

Label 1003.2.p
Level $1003$
Weight $2$
Character orbit 1003.p
Rep. character $\chi_{1003}(4,\cdot)$
Character field $\Q(\zeta_{116})$
Dimension $4928$
Sturm bound $180$

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Defining parameters

Level: \( N \) \(=\) \( 1003 = 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1003.p (of order \(116\) and degree \(56\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1003 \)
Character field: \(\Q(\zeta_{116})\)
Sturm bound: \(180\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1003, [\chi])\).

Total New Old
Modular forms 5152 5152 0
Cusp forms 4928 4928 0
Eisenstein series 224 224 0

Trace form

\( 4928 q - 58 q^{3} + 64 q^{4} - 54 q^{5} - 66 q^{6} - 54 q^{7} + O(q^{10}) \) \( 4928 q - 58 q^{3} + 64 q^{4} - 54 q^{5} - 66 q^{6} - 54 q^{7} - 62 q^{10} - 54 q^{11} - 58 q^{12} - 108 q^{13} - 58 q^{14} - 288 q^{16} - 42 q^{17} - 112 q^{18} - 62 q^{20} - 96 q^{21} - 66 q^{22} - 42 q^{23} - 26 q^{24} - 76 q^{27} - 98 q^{28} - 66 q^{29} - 76 q^{30} - 50 q^{31} - 140 q^{33} - 90 q^{34} - 92 q^{35} - 34 q^{37} - 156 q^{38} - 34 q^{39} - 6 q^{40} - 82 q^{41} - 54 q^{44} - 84 q^{45} - 114 q^{46} - 116 q^{47} - 58 q^{48} - 368 q^{50} - 42 q^{51} + 364 q^{52} - 472 q^{54} - 108 q^{55} + 378 q^{56} + 4 q^{57} - 60 q^{58} - 62 q^{61} - 94 q^{62} - 50 q^{63} + 104 q^{64} - 38 q^{65} - 264 q^{67} - 138 q^{68} + 356 q^{69} - 152 q^{71} - 192 q^{72} - 52 q^{73} - 78 q^{74} - 54 q^{75} + 50 q^{78} - 6 q^{79} - 38 q^{80} + 92 q^{81} - 62 q^{82} - 100 q^{84} - 86 q^{85} - 156 q^{86} - 82 q^{88} - 172 q^{89} - 190 q^{90} - 82 q^{91} - 78 q^{92} - 82 q^{95} - 134 q^{96} + 2 q^{97} - 272 q^{98} - 300 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1003, [\chi])\) into newform subspaces

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