Properties

Label 1008.2.x
Level 1008
Weight 2
Character orbit x
Rep. character \(\chi_{1008}(307,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 156
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.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 112 \)
Character field: \(\Q(i)\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 400 164 236
Cusp forms 368 156 212
Eisenstein series 32 8 24

Trace form

\( 156q + 4q^{2} - 2q^{4} - 4q^{7} - 8q^{8} + O(q^{10}) \) \( 156q + 4q^{2} - 2q^{4} - 4q^{7} - 8q^{8} + 14q^{14} - 6q^{16} - 26q^{22} + 16q^{23} - 8q^{28} - 4q^{29} + 24q^{32} - 20q^{35} - 12q^{37} - 22q^{44} + 8q^{46} - 4q^{49} + 22q^{50} - 4q^{53} + 50q^{56} - 6q^{58} - 50q^{64} + 8q^{65} - 32q^{67} + 32q^{70} + 72q^{71} + 62q^{74} + 16q^{77} + 16q^{85} - 62q^{86} + 38q^{88} - 28q^{91} - 48q^{92} + 4q^{98} + O(q^{100}) \)

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