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Properties

Label 3744.2.ca
Level $3744$
Weight $2$
Character orbit 3744.ca
Rep. character $\chi_{3744}(49,\cdot)$
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.ca (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

\( 328 q - 2 q^{9} + O(q^{10}) \) \( 328 q - 2 q^{9} - 12 q^{15} - 4 q^{17} - 44 q^{23} - 152 q^{25} - 6 q^{33} + 4 q^{39} - 284 q^{49} - 6 q^{55} + 6 q^{63} + 18 q^{65} + 12 q^{71} + 4 q^{79} - 2 q^{81} + 2 q^{87} - 12 q^{89} - 76 q^{95} + O(q^{100}) \)

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

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