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Properties

Label 3344.2.dz
Level $3344$
Weight $2$
Character orbit 3344.dz
Rep. character $\chi_{3344}(31,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $960$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 3344 = 2^{4} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3344.dz (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 836 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3344, [\chi])\).

Total New Old
Modular forms 3936 960 2976
Cusp forms 3744 960 2784
Eisenstein series 192 0 192

Trace form

\( 960 q + 132 q^{9} + O(q^{10}) \) \( 960 q + 132 q^{9} + 24 q^{17} + 120 q^{25} - 72 q^{33} + 72 q^{41} + 312 q^{49} + 72 q^{53} - 30 q^{57} + 24 q^{61} + 36 q^{73} - 72 q^{77} + 54 q^{81} + 48 q^{85} - 72 q^{89} + 144 q^{93} + 198 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3344, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3344, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(836, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1672, [\chi])\)\(^{\oplus 2}\)