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Properties

Label 3640.2.cj
Level $3640$
Weight $2$
Character orbit 3640.cj
Rep. character $\chi_{3640}(3333,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $1008$
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.cj (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 520 \)
Character field: \(\Q(i)\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1360 1008 352
Cusp forms 1328 1008 320
Eisenstein series 32 0 32

Trace form

\( 1008 q + O(q^{10}) \) \( 1008 q + 16 q^{12} + 16 q^{17} - 20 q^{20} + 56 q^{22} + 32 q^{24} - 32 q^{26} + 16 q^{40} + 32 q^{44} + 1008 q^{49} - 32 q^{50} + 32 q^{54} + 48 q^{58} - 28 q^{60} - 32 q^{65} + 104 q^{68} + 24 q^{70} - 32 q^{76} - 28 q^{78} - 1008 q^{81} - 16 q^{82} + 32 q^{86} + 64 q^{88} - 64 q^{90} - 32 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)