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Properties

Label 3344.2.z
Level $3344$
Weight $2$
Character orbit 3344.z
Rep. character $\chi_{3344}(609,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $432$
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.z (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1968 432 1536
Cusp forms 1872 432 1440
Eisenstein series 96 0 96

Trace form

\( 432 q + 4 q^{7} - 108 q^{9} + O(q^{10}) \) \( 432 q + 4 q^{7} - 108 q^{9} + 4 q^{11} - 12 q^{15} - 6 q^{19} - 4 q^{23} - 92 q^{25} - 12 q^{27} - 16 q^{29} + 8 q^{33} - 6 q^{35} + 24 q^{37} + 88 q^{39} + 88 q^{43} + 24 q^{47} - 92 q^{49} + 72 q^{51} + 24 q^{53} + 40 q^{55} - 8 q^{59} + 20 q^{63} + 40 q^{67} + 32 q^{69} - 44 q^{71} - 24 q^{73} - 60 q^{75} + 8 q^{77} - 84 q^{79} - 108 q^{81} - 48 q^{83} - 168 q^{87} - 56 q^{91} + 32 q^{93} + 16 q^{95} - 16 q^{97} - 124 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(418, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(836, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1672, [\chi])\)\(^{\oplus 2}\)