Properties

Label 1512.2.eb
Level 1512
Weight 2
Character orbit eb
Rep. character \(\chi_{1512}(347,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 1704
Sturm bound 576

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Defining parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.eb (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 1512 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1512, [\chi])\).

Total New Old
Modular forms 1752 1752 0
Cusp forms 1704 1704 0
Eisenstein series 48 48 0

Trace form

\( 1704q - 3q^{2} - 6q^{3} - 3q^{4} - 12q^{6} - 18q^{8} - 6q^{9} + O(q^{10}) \) \( 1704q - 3q^{2} - 6q^{3} - 3q^{4} - 12q^{6} - 18q^{8} - 6q^{9} + 3q^{10} - 6q^{11} - 3q^{12} - 36q^{14} - 3q^{16} - 18q^{17} - 3q^{18} + 6q^{19} - 12q^{20} - 12q^{22} + 66q^{24} - 6q^{25} - 24q^{27} - 12q^{28} + 15q^{30} + 57q^{32} - 6q^{33} - 6q^{34} - 18q^{35} + 18q^{36} - 51q^{38} + 27q^{40} - 24q^{41} - 21q^{42} - 24q^{43} - 6q^{46} + 54q^{48} - 12q^{49} + 3q^{50} - 42q^{51} - 3q^{52} + 39q^{54} + 57q^{56} - 42q^{57} - 3q^{58} - 6q^{59} - 63q^{60} - 117q^{62} - 6q^{64} - 6q^{65} - 3q^{66} - 6q^{67} - 42q^{68} - 33q^{70} - 9q^{72} - 12q^{73} + 63q^{74} - 6q^{75} - 24q^{76} - 30q^{78} - 6q^{81} - 6q^{82} + 36q^{83} - 21q^{84} - 117q^{86} + 21q^{88} - 18q^{89} - 39q^{90} - 6q^{91} - 72q^{92} - 3q^{94} + 213q^{96} - 24q^{97} - 180q^{98} - 24q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1512, [\chi])\) 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