Properties

Label 1584.2.dh
Level $1584$
Weight $2$
Character orbit 1584.dh
Rep. character $\chi_{1584}(79,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $576$
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.dh (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 396 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 2400 576 1824
Cusp forms 2208 576 1632
Eisenstein series 192 0 192

Trace form

\( 576 q - 12 q^{9} + O(q^{10}) \) \( 576 q - 12 q^{9} + 72 q^{25} + 36 q^{33} + 48 q^{45} + 72 q^{49} + 24 q^{53} - 60 q^{57} + 84 q^{69} + 24 q^{77} + 12 q^{81} - 48 q^{89} + 72 q^{93} + 54 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1584, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 3}\)