Properties

Label 1512.2.eu
Level 1512
Weight 2
Character orbit eu
Rep. character \(\chi_{1512}(277,\cdot)\)
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.eu (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

\( 1704q - 3q^{2} - 3q^{4} - 12q^{6} - 12q^{7} - 6q^{8} - 6q^{9} + O(q^{10}) \) \( 1704q - 3q^{2} - 3q^{4} - 12q^{6} - 12q^{7} - 6q^{8} - 6q^{9} - 6q^{10} - 3q^{12} - 21q^{14} - 24q^{15} - 3q^{16} - 12q^{17} - 3q^{18} - 12q^{20} - 12q^{22} - 6q^{23} + 9q^{24} - 6q^{25} - 6q^{26} - 12q^{28} + 33q^{30} - 6q^{31} - 33q^{32} - 6q^{33} - 18q^{34} + 18q^{36} + 51q^{38} - 6q^{39} + 12q^{40} - 24q^{41} + 9q^{42} + 3q^{44} + 3q^{46} - 6q^{47} - 78q^{48} - 12q^{49} + 3q^{50} - 3q^{52} - 45q^{54} - 48q^{55} - 27q^{56} - 6q^{57} - 3q^{58} + 27q^{60} + 27q^{62} - 72q^{63} - 6q^{64} - 6q^{65} - 3q^{66} - 36q^{68} - 36q^{70} - 12q^{71} - 111q^{72} + 6q^{73} - 99q^{74} - 30q^{78} - 6q^{79} - 6q^{80} - 6q^{81} - 6q^{82} - 96q^{84} - 81q^{86} - 6q^{87} - 51q^{88} - 12q^{89} - 39q^{90} - 72q^{92} - 3q^{94} + 114q^{95} + 105q^{96} - 24q^{97} - 117q^{98} + O(q^{100}) \)

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