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Properties

Label 1003.2.e
Level $1003$
Weight $2$
Character orbit 1003.e
Rep. character $\chi_{1003}(591,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $176$
Sturm bound $180$

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Defining parameters

Level: \( N \) \(=\) \( 1003 = 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1003.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(i)\)
Sturm bound: \(180\)

Dimensions

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

Total New Old
Modular forms 184 176 8
Cusp forms 176 176 0
Eisenstein series 8 0 8

Trace form

\( 176 q - 180 q^{4} - 4 q^{5} + 8 q^{6} - 4 q^{7} + O(q^{10}) \) \( 176 q - 180 q^{4} - 4 q^{5} + 8 q^{6} - 4 q^{7} + 4 q^{10} - 4 q^{11} - 8 q^{13} + 172 q^{16} - 16 q^{17} - 4 q^{18} + 4 q^{20} - 20 q^{21} + 8 q^{22} - 16 q^{23} - 32 q^{24} + 18 q^{27} + 40 q^{28} + 8 q^{29} - 40 q^{30} - 8 q^{31} + 24 q^{33} + 32 q^{34} - 24 q^{35} - 24 q^{37} + 40 q^{38} - 24 q^{39} - 52 q^{40} + 24 q^{41} - 4 q^{44} + 26 q^{45} + 56 q^{46} + 20 q^{50} - 16 q^{51} - 16 q^{52} + 8 q^{54} - 8 q^{55} + 28 q^{56} - 62 q^{57} - 56 q^{58} + 4 q^{61} + 36 q^{62} - 8 q^{63} - 220 q^{64} - 20 q^{65} + 32 q^{67} + 80 q^{68} - 8 q^{69} - 22 q^{71} + 76 q^{72} + 52 q^{73} + 20 q^{74} - 4 q^{75} - 108 q^{78} - 52 q^{79} - 20 q^{80} - 208 q^{81} + 4 q^{82} - 16 q^{84} + 28 q^{85} + 40 q^{86} + 24 q^{88} + 56 q^{89} + 132 q^{90} + 24 q^{91} + 20 q^{92} + 24 q^{95} + 76 q^{96} - 60 q^{97} + 156 q^{98} + 68 q^{99} + O(q^{100}) \)

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.