Properties

Label 1003.2.g
Level 1003
Weight 2
Character orbit g
Rep. character \(\chi_{1003}(60,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 344
Sturm bound 180

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1003 = 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1003.g (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(180\)

Dimensions

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

Total New Old
Modular forms 368 344 24
Cusp forms 352 344 8
Eisenstein series 16 0 16

Trace form

\( 344q - 8q^{5} - 16q^{6} + O(q^{10}) \) \( 344q - 8q^{5} - 16q^{6} - 16q^{10} + 8q^{11} - 4q^{15} - 320q^{16} + 32q^{18} - 32q^{19} + 16q^{20} - 48q^{22} + 16q^{24} - 16q^{26} - 48q^{27} + 16q^{28} + 8q^{29} - 16q^{31} + 40q^{32} - 48q^{33} + 64q^{34} - 64q^{35} + 64q^{36} - 32q^{37} + 16q^{39} + 32q^{40} - 8q^{41} + 96q^{42} + 16q^{43} + 64q^{44} - 52q^{45} - 80q^{46} - 40q^{49} - 80q^{50} + 16q^{51} + 64q^{52} + 8q^{53} - 64q^{54} - 56q^{56} - 56q^{61} + 16q^{62} + 16q^{63} + 72q^{65} - 16q^{66} - 64q^{67} + 40q^{68} + 112q^{69} + 56q^{70} - 32q^{71} + 80q^{73} - 96q^{74} - 8q^{75} + 120q^{76} - 80q^{77} - 48q^{78} - 8q^{80} + 64q^{82} + 32q^{83} - 96q^{84} - 64q^{85} + 32q^{86} + 8q^{88} - 32q^{90} + 80q^{91} + 192q^{92} - 152q^{93} - 16q^{94} + 8q^{95} + 16q^{96} - 72q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1003, [\chi])\) into irreducible Hecke orbits

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

Decomposition of \(S_{2}^{\mathrm{old}}(1003, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1003, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 2}\)