Properties

Label 1512.2.de
Level 1512
Weight 2
Character orbit de
Rep. character \(\chi_{1512}(25,\cdot)\)
Character field \(\Q(\zeta_{9})\)
Dimension 432
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.de (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 189 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 1776 432 1344
Cusp forms 1680 432 1248
Eisenstein series 96 0 96

Trace form

\( 432q + O(q^{10}) \) \( 432q + 12q^{15} - 48q^{17} - 24q^{21} + 12q^{23} + 18q^{29} + 72q^{39} + 12q^{41} - 36q^{45} - 18q^{47} + 18q^{49} + 36q^{61} + 18q^{63} - 36q^{65} + 48q^{69} + 36q^{75} - 12q^{77} - 36q^{81} - 144q^{89} - 36q^{93} + 54q^{95} - 108q^{99} + O(q^{100}) \)

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

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

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

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database