Properties

Label 1512.2.dc
Level 1512
Weight 2
Character orbit dc
Rep. character \(\chi_{1512}(169,\cdot)\)
Character field \(\Q(\zeta_{9})\)
Dimension 324
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.dc (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 27 \)
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 324 1452
Cusp forms 1680 324 1356
Eisenstein series 96 0 96

Trace form

\( 324q + O(q^{10}) \) \( 324q - 6q^{11} - 12q^{15} - 12q^{23} + 30q^{27} + 18q^{33} + 36q^{35} + 36q^{39} + 18q^{41} - 18q^{43} + 72q^{45} + 36q^{47} + 84q^{51} + 72q^{53} + 90q^{57} + 84q^{59} + 108q^{65} - 18q^{67} - 12q^{81} - 60q^{83} - 60q^{87} - 18q^{89} - 72q^{93} - 60q^{95} + 54q^{97} - 60q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database