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Properties

Label 3744.2.dj
Level $3744$
Weight $2$
Character orbit 3744.dj
Rep. character $\chi_{3744}(1535,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $288$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3744.dj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3744, [\chi])\).

Total New Old
Modular forms 1376 288 1088
Cusp forms 1312 288 1024
Eisenstein series 64 0 64

Trace form

\( 288 q + 8 q^{9} + O(q^{10}) \) \( 288 q + 8 q^{9} - 16 q^{21} + 144 q^{25} - 48 q^{29} + 40 q^{33} + 72 q^{41} + 16 q^{45} + 144 q^{49} + 40 q^{57} - 32 q^{69} - 48 q^{73} - 24 q^{81} + 96 q^{93} - 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3744, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3744, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3744, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)