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Properties

Label 3696.2.bp
Level $3696$
Weight $2$
Character orbit 3696.bp
Rep. character $\chi_{3696}(1693,\cdot)$
Character field $\Q(\zeta_{4})$
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.bp (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1232 \)
Character field: \(\Q(i)\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 1552 768 784
Cusp forms 1520 768 752
Eisenstein series 32 0 32

Trace form

\( 768 q - 8 q^{4} + O(q^{10}) \) \( 768 q - 8 q^{4} - 8 q^{11} - 16 q^{14} + 8 q^{16} + 28 q^{22} - 32 q^{37} + 4 q^{44} - 32 q^{53} + 8 q^{58} + 24 q^{60} + 40 q^{64} - 16 q^{67} + 16 q^{70} + 72 q^{78} - 768 q^{81} + 88 q^{86} - 92 q^{88} + 16 q^{91} + 112 q^{92} + 8 q^{99} + O(q^{100}) \)

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

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