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Properties

Label 3696.2.fj
Level $3696$
Weight $2$
Character orbit 3696.fj
Rep. character $\chi_{3696}(323,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $4608$
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.fj (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 528 \)
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 4608 1600
Cusp forms 6080 4608 1472
Eisenstein series 128 0 128

Trace form

\( 4608 q + O(q^{10}) \) \( 4608 q + 32 q^{16} + 16 q^{22} + 64 q^{24} + 64 q^{43} - 64 q^{46} - 1152 q^{49} - 16 q^{52} + 64 q^{55} + 32 q^{58} + 92 q^{66} + 64 q^{67} + 24 q^{70} - 180 q^{72} + 256 q^{76} + 104 q^{78} + 120 q^{82} + 424 q^{88} + 120 q^{90} + 64 q^{96} - 64 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3696, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 2}\)