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Properties

Label 3696.2.cq
Level $3696$
Weight $2$
Character orbit 3696.cq
Rep. character $\chi_{3696}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $376$
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.cq (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 1584 392 1192
Cusp forms 1488 376 1112
Eisenstein series 96 16 80

Trace form

\( 376 q + 2 q^{3} - 2 q^{9} + O(q^{10}) \) \( 376 q + 2 q^{3} - 2 q^{9} + 20 q^{15} + 176 q^{25} + 8 q^{27} + 4 q^{31} - 7 q^{33} - 4 q^{37} - 22 q^{45} - 16 q^{49} + 28 q^{55} - 28 q^{67} + 12 q^{69} - 20 q^{75} - 2 q^{81} - 24 q^{91} - 6 q^{93} - 32 q^{97} + 34 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3696, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(924, [\chi])\)\(^{\oplus 3}\)