Properties

Label 1512.2.dx
Level 1512
Weight 2
Character orbit dx
Rep. character \(\chi_{1512}(85,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 1296
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.dx (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 216 \)
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 1296 456
Cusp forms 1704 1296 408
Eisenstein series 48 0 48

Trace form

\( 1296q + O(q^{10}) \) \( 1296q - 18q^{12} + 42q^{18} - 42q^{20} + 36q^{26} + 48q^{30} + 30q^{32} - 24q^{33} + 24q^{41} + 30q^{42} - 48q^{44} + 18q^{48} + 156q^{50} + 54q^{52} - 54q^{58} - 186q^{60} + 6q^{66} - 78q^{68} + 168q^{71} - 42q^{72} - 180q^{80} - 30q^{86} + 72q^{87} + 30q^{90} - 114q^{92} + 54q^{94} - 156q^{96} + O(q^{100}) \)

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

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

Decomposition of \(S_{2}^{\mathrm{old}}(1512, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database