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Properties

Label 3696.2.ga
Level $3696$
Weight $2$
Character orbit 3696.ga
Rep. character $\chi_{3696}(31,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $768$
Sturm bound $1536$

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Defining parameters

Level: \( N \) \(=\) \( 3696 = 2^{4} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3696.ga (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 308 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1536\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3696, [\chi])\).

Total New Old
Modular forms 6336 768 5568
Cusp forms 5952 768 5184
Eisenstein series 384 0 384

Trace form

\( 768 q + 96 q^{9} + O(q^{10}) \) \( 768 q + 96 q^{9} - 120 q^{25} - 36 q^{33} - 120 q^{49} + 48 q^{53} + 144 q^{61} + 48 q^{65} + 120 q^{77} + 96 q^{81} + 48 q^{85} - 72 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3696, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3696, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3696, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(616, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(924, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1232, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1848, [\chi])\)\(^{\oplus 2}\)