Properties

Label 3744.2.cz
Level $3744$
Weight $2$
Character orbit 3744.cz
Rep. character $\chi_{3744}(1777,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $328$
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.cz (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 936 \)
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 344 1032
Cusp forms 1312 328 984
Eisenstein series 64 16 48

Trace form

\( 328 q - 2 q^{7} - 2 q^{9} + O(q^{10}) \) \( 328 q - 2 q^{7} - 2 q^{9} + 14 q^{15} - 4 q^{17} + 22 q^{23} + 144 q^{25} + 4 q^{31} + 22 q^{33} - 2 q^{39} + 2 q^{41} + 4 q^{47} - 138 q^{49} + 14 q^{55} - 20 q^{57} - 26 q^{63} - 22 q^{65} + 4 q^{71} - 16 q^{73} + 4 q^{79} - 2 q^{81} - 34 q^{87} - 4 q^{89} + 112 q^{95} + 2 q^{97} + O(q^{100}) \)

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

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