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Properties

Label 3640.2.ph
Level $3640$
Weight $2$
Character orbit 3640.ph
Rep. character $\chi_{3640}(11,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1792$
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.ph (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 728 \)
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 1792 928
Cusp forms 2656 1792 864
Eisenstein series 64 0 64

Trace form

\( 1792 q + 1792 q^{9} + O(q^{10}) \) \( 1792 q + 1792 q^{9} - 16 q^{14} + 16 q^{20} - 48 q^{24} + 20 q^{26} + 44 q^{28} - 20 q^{32} + 32 q^{34} - 120 q^{38} - 32 q^{42} - 8 q^{44} - 40 q^{46} - 80 q^{48} + 64 q^{57} + 64 q^{59} - 40 q^{66} + 8 q^{70} + 112 q^{72} + 32 q^{73} - 56 q^{74} + 1792 q^{81} + 36 q^{84} - 64 q^{86} - 64 q^{91} - 8 q^{92} - 48 q^{94} - 72 q^{96} - 64 q^{97} - 56 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)