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Properties

Label 3640.2.nl
Level $3640$
Weight $2$
Character orbit 3640.nl
Rep. character $\chi_{3640}(43,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2016$
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.nl (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 520 \)
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 2016 704
Cusp forms 2656 2016 640
Eisenstein series 64 0 64

Trace form

\( 2016 q + O(q^{10}) \) \( 2016 q + 16 q^{10} + 32 q^{12} - 8 q^{17} - 4 q^{22} + 16 q^{25} + 32 q^{26} + 16 q^{30} + 60 q^{32} - 32 q^{36} - 8 q^{40} - 64 q^{43} + 52 q^{48} - 60 q^{50} + 72 q^{58} - 40 q^{62} - 16 q^{65} - 128 q^{66} - 52 q^{68} + 76 q^{78} + 1008 q^{81} - 16 q^{82} - 88 q^{88} + 40 q^{92} + O(q^{100}) \)

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

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