Properties

Label 1008.2.em
Level 1008
Weight 2
Character orbit em
Rep. character \(\chi_{1008}(293,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 752
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.em (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 1008 \)
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 784 784 0
Cusp forms 752 752 0
Eisenstein series 32 32 0

Trace form

\( 752q - 12q^{2} - 4q^{4} + O(q^{10}) \) \( 752q - 12q^{2} - 4q^{4} - 12q^{11} - 6q^{14} - 16q^{15} - 4q^{16} + 20q^{18} + 2q^{21} - 4q^{22} - 24q^{28} - 12q^{29} + 4q^{30} - 12q^{32} - 4q^{36} - 16q^{37} + 48q^{42} - 4q^{43} - 4q^{49} - 12q^{50} + 8q^{51} - 48q^{56} - 4q^{58} + 24q^{60} - 36q^{63} - 16q^{64} - 24q^{65} - 4q^{67} - 16q^{70} - 16q^{72} - 96q^{74} - 6q^{77} - 76q^{78} - 8q^{79} - 16q^{81} - 138q^{84} - 24q^{85} + 48q^{86} - 4q^{88} + 20q^{91} - 12q^{92} - 20q^{93} - 24q^{95} + 28q^{99} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database