Properties

Label 1008.2.ec
Level 1008
Weight 2
Character orbit ec
Rep. character \(\chi_{1008}(19,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 312
Sturm bound 384

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Defining parameters

Level: \( N \) = \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1008.ec (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1008, [\chi])\).

Total New Old
Modular forms 800 328 472
Cusp forms 736 312 424
Eisenstein series 64 16 48

Trace form

\( 312q + 2q^{2} - 4q^{4} + 6q^{5} - 8q^{7} + 20q^{8} + O(q^{10}) \) \( 312q + 2q^{2} - 4q^{4} + 6q^{5} - 8q^{7} + 20q^{8} - 24q^{10} + 6q^{11} + 16q^{14} + 12q^{17} - 6q^{19} + 20q^{22} - 4q^{23} + 6q^{26} + 2q^{28} - 8q^{29} + 12q^{32} + 26q^{35} + 6q^{37} + 6q^{38} + 54q^{40} - 14q^{44} + 16q^{46} - 8q^{49} + 32q^{50} + 12q^{52} + 10q^{53} + 40q^{56} - 6q^{58} + 54q^{59} - 6q^{61} + 80q^{64} + 4q^{65} - 10q^{67} + 36q^{68} - 32q^{70} - 48q^{71} + 10q^{74} - 10q^{77} + 24q^{80} - 78q^{82} - 28q^{85} + 44q^{86} + 22q^{88} + 64q^{91} - 36q^{92} + 30q^{94} - 40q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database