Properties

Label 3240.2.dh
Level $3240$
Weight $2$
Character orbit 3240.dh
Rep. character $\chi_{3240}(49,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $2916$
Sturm bound $1296$

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Defining parameters

Level: \( N \) \(=\) \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3240.dh (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 405 \)
Character field: \(\Q(\zeta_{54})\)
Sturm bound: \(1296\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3240, [\chi])\).

Total New Old
Modular forms 11808 2916 8892
Cusp forms 11520 2916 8604
Eisenstein series 288 0 288

Trace form

\( 2916 q + O(q^{10}) \) \( 2916 q + 18 q^{41} - 54 q^{45} + 108 q^{51} - 108 q^{59} - 54 q^{65} - 18 q^{69} + 162 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3240, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(810, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1620, [\chi])\)\(^{\oplus 2}\)