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Properties

Label 3696.2.ew
Level $3696$
Weight $2$
Character orbit 3696.ew
Rep. character $\chi_{3696}(683,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2560$
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.ew (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 336 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 3104 2560 544
Cusp forms 3040 2560 480
Eisenstein series 64 0 64

Trace form

\( 2560 q + O(q^{10}) \) \( 2560 q - 20 q^{18} + 40 q^{24} + 40 q^{30} - 64 q^{34} - 80 q^{36} - 24 q^{40} + 80 q^{48} - 40 q^{51} + 32 q^{58} + 40 q^{60} + 20 q^{66} - 192 q^{70} + 56 q^{72} + 192 q^{76} + 152 q^{78} + 40 q^{82} + 76 q^{84} - 144 q^{90} - 76 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3696, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)