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Properties

Label 1584.2.bl
Level $1584$
Weight $2$
Character orbit 1584.bl
Rep. character $\chi_{1584}(815,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1584.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1584, [\chi])\).

Total New Old
Modular forms 600 120 480
Cusp forms 552 120 432
Eisenstein series 48 0 48

Trace form

\( 120 q + O(q^{10}) \) \( 120 q + 24 q^{21} + 60 q^{25} + 72 q^{29} + 60 q^{45} + 60 q^{49} - 48 q^{57} - 144 q^{65} - 36 q^{69} - 120 q^{81} + 24 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1584, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1584, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1584, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)