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Properties

Label 3640.2.lj
Level $3640$
Weight $2$
Character orbit 3640.lj
Rep. character $\chi_{3640}(443,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2304$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3640.lj (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3640, [\chi])\).

Total New Old
Modular forms 2720 2304 416
Cusp forms 2656 2304 352
Eisenstein series 64 0 64

Trace form

\( 2304 q + 24 q^{8} + O(q^{10}) \) \( 2304 q + 24 q^{8} + 76 q^{28} + 40 q^{30} - 40 q^{32} + 48 q^{35} + 12 q^{38} - 48 q^{46} - 64 q^{48} - 80 q^{50} + 56 q^{56} - 32 q^{58} + 40 q^{60} + 64 q^{66} + 48 q^{67} + 44 q^{68} - 120 q^{70} + 100 q^{72} + 192 q^{76} + 1120 q^{81} - 120 q^{82} + 48 q^{86} + 44 q^{88} + 120 q^{90} + 56 q^{96} + 64 q^{97} + 32 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3640, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3640, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)