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Properties

Label 3744.2.gf
Level $3744$
Weight $2$
Character orbit 3744.gf
Rep. character $\chi_{3744}(1553,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $656$
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.gf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 936 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 2752 688 2064
Cusp forms 2624 656 1968
Eisenstein series 128 32 96

Trace form

\( 656 q + 4 q^{7} - 4 q^{9} + O(q^{10}) \) \( 656 q + 4 q^{7} - 4 q^{9} - 4 q^{15} + 12 q^{23} + 4 q^{31} - 32 q^{33} + 20 q^{39} - 12 q^{41} + 12 q^{47} - 12 q^{49} + 8 q^{55} - 20 q^{57} - 20 q^{63} - 12 q^{65} - 16 q^{73} + 8 q^{79} - 4 q^{81} + 76 q^{87} + 24 q^{95} - 4 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3744, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1872, [\chi])\)\(^{\oplus 2}\)