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Properties

Label 3344.2.cf
Level $3344$
Weight $2$
Character orbit 3344.cf
Rep. character $\chi_{3344}(45,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1600$
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.cf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1936 1600 336
Cusp forms 1904 1600 304
Eisenstein series 32 0 32

Trace form

\( 1600 q + 24 q^{8} + O(q^{10}) \) \( 1600 q + 24 q^{8} - 4 q^{10} + 32 q^{15} - 8 q^{16} + 16 q^{19} + 56 q^{20} - 16 q^{24} - 40 q^{28} - 112 q^{30} + 96 q^{31} + 16 q^{34} - 48 q^{35} - 32 q^{36} + 12 q^{38} + 20 q^{42} - 16 q^{46} + 40 q^{48} - 1600 q^{49} + 48 q^{50} + 16 q^{51} + 32 q^{54} + 16 q^{56} + 56 q^{58} - 20 q^{60} - 64 q^{61} - 24 q^{62} - 24 q^{64} - 20 q^{66} + 48 q^{67} + 88 q^{68} + 128 q^{69} + 144 q^{70} - 56 q^{72} - 56 q^{74} - 224 q^{75} - 4 q^{76} - 24 q^{78} - 64 q^{79} - 4 q^{80} + 800 q^{81} + 20 q^{82} - 32 q^{85} - 64 q^{86} + 72 q^{90} + 24 q^{92} - 32 q^{94} + 48 q^{95} + 416 q^{96} - 132 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)