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Properties

Label 3640.2.ln
Level $3640$
Weight $2$
Character orbit 3640.ln
Rep. character $\chi_{3640}(1633,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $672$
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.ln (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 455 \)
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 2752 672 2080
Cusp forms 2624 672 1952
Eisenstein series 128 0 128

Trace form

\( 672 q + O(q^{10}) \) \( 672 q + 4 q^{11} - 16 q^{15} - 4 q^{19} - 16 q^{23} - 24 q^{27} - 24 q^{35} - 24 q^{41} + 48 q^{49} + 96 q^{57} - 8 q^{59} + 4 q^{65} + 32 q^{67} - 48 q^{71} + 32 q^{73} - 48 q^{77} + 336 q^{81} - 24 q^{89} + 32 q^{95} + 48 q^{97} - 88 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(455, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(910, [\chi])\)\(^{\oplus 3}\)