Properties

Label 2736.3.dg
Level $2736$
Weight $3$
Character orbit 2736.dg
Rep. character $\chi_{2736}(463,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $480$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2736.dg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 684 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2736, [\chi])\).

Total New Old
Modular forms 1944 480 1464
Cusp forms 1896 480 1416
Eisenstein series 48 0 48

Trace form

\( 480q + 12q^{9} + O(q^{10}) \) \( 480q + 12q^{9} - 72q^{17} + 2400q^{25} + 36q^{33} - 72q^{41} + 1680q^{49} + 300q^{57} + 144q^{65} - 36q^{73} - 564q^{81} - 432q^{89} - 180q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 3}\)