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Properties

Label 3640.2.hb
Level $3640$
Weight $2$
Character orbit 3640.hb
Rep. character $\chi_{3640}(2131,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $896$
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.hb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 728 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1360 896 464
Cusp forms 1328 896 432
Eisenstein series 32 0 32

Trace form

\( 896 q + 448 q^{9} + O(q^{10}) \) \( 896 q + 448 q^{9} - 16 q^{14} - 8 q^{16} + 48 q^{22} + 448 q^{25} - 30 q^{26} + 40 q^{36} - 60 q^{38} - 44 q^{42} + 32 q^{49} + 36 q^{52} + 56 q^{56} + 48 q^{64} + 60 q^{66} - 60 q^{68} + 56 q^{74} + 32 q^{78} - 448 q^{81} - 60 q^{82} + 64 q^{91} + 80 q^{92} - 36 q^{94} + O(q^{100}) \)

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

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