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Properties

Label 3344.2.q
Level $3344$
Weight $2$
Character orbit 3344.q
Rep. character $\chi_{3344}(353,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $200$
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.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 984 200 784
Cusp forms 936 200 736
Eisenstein series 48 0 48

Trace form

\( 200 q - 4 q^{3} - 8 q^{7} - 100 q^{9} + O(q^{10}) \) \( 200 q - 4 q^{3} - 8 q^{7} - 100 q^{9} + 8 q^{15} + 16 q^{19} - 100 q^{25} + 32 q^{27} - 40 q^{31} + 24 q^{35} - 8 q^{39} + 16 q^{43} - 12 q^{47} + 184 q^{49} - 8 q^{51} + 8 q^{57} - 36 q^{59} - 32 q^{61} + 52 q^{63} + 32 q^{65} + 16 q^{67} + 64 q^{69} + 40 q^{71} + 8 q^{73} - 128 q^{75} + 44 q^{79} - 68 q^{81} + 48 q^{83} + 16 q^{85} + 56 q^{87} - 4 q^{89} - 64 q^{91} + 60 q^{95} - 20 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(418, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(836, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1672, [\chi])\)\(^{\oplus 2}\)