Properties

Label 1512.2.eg
Level 1512
Weight 2
Character orbit eg
Rep. character \(\chi_{1512}(155,\cdot)\)
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.eg (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

\( 1296q + O(q^{10}) \) \( 1296q + 18q^{12} - 42q^{18} + 42q^{20} + 48q^{30} + 30q^{32} + 24q^{33} - 24q^{41} + 30q^{42} + 144q^{44} + 18q^{48} - 156q^{50} - 54q^{52} + 54q^{58} + 72q^{59} + 126q^{60} - 186q^{66} - 78q^{68} - 42q^{72} - 84q^{74} + 168q^{75} - 156q^{78} - 30q^{86} - 198q^{90} + 114q^{92} + 54q^{94} - 156q^{96} + O(q^{100}) \)

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