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Properties

Label 3344.2.bi
Level $3344$
Weight $2$
Character orbit 3344.bi
Rep. character $\chi_{3344}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $236$
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.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 209 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 984 244 740
Cusp forms 936 236 700
Eisenstein series 48 8 40

Trace form

\( 236 q + 6 q^{3} - 2 q^{5} + 116 q^{9} + O(q^{10}) \) \( 236 q + 6 q^{3} - 2 q^{5} + 116 q^{9} + 4 q^{11} + 6 q^{15} + 14 q^{23} - 112 q^{25} - 6 q^{33} + 2 q^{47} - 236 q^{49} - 30 q^{53} + 6 q^{59} - 66 q^{67} + 6 q^{71} + 16 q^{77} - 114 q^{81} + 6 q^{89} - 36 q^{91} + 36 q^{93} + 42 q^{97} + 32 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(418, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(836, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1672, [\chi])\)\(^{\oplus 2}\)