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Properties

Label 3696.2.fc
Level $3696$
Weight $2$
Character orbit 3696.fc
Rep. character $\chi_{3696}(13,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $3072$
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.fc (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1232 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 6208 3072 3136
Cusp forms 6080 3072 3008
Eisenstein series 128 0 128

Trace form

\( 3072 q + 8 q^{4} + O(q^{10}) \) \( 3072 q + 8 q^{4} + 8 q^{11} + 16 q^{14} - 8 q^{16} + 20 q^{18} + 92 q^{22} - 48 q^{37} - 4 q^{44} - 48 q^{53} - 8 q^{58} - 24 q^{60} + 200 q^{64} + 16 q^{67} - 16 q^{70} + 20 q^{72} + 48 q^{78} + 768 q^{81} - 120 q^{84} + 212 q^{86} + 92 q^{88} + 104 q^{91} + 188 q^{92} + 32 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3696, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1232, [\chi])\)\(^{\oplus 2}\)