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Properties

Label 1344.2.cj
Level $1344$
Weight $2$
Character orbit 1344.cj
Rep. character $\chi_{1344}(125,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $2016$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1344.cj (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1344 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1344, [\chi])\).

Total New Old
Modular forms 2080 2080 0
Cusp forms 2016 2016 0
Eisenstein series 64 64 0

Trace form

\( 2016 q - 32 q^{4} - 16 q^{7} - 16 q^{9} + O(q^{10}) \) \( 2016 q - 32 q^{4} - 16 q^{7} - 16 q^{9} - 16 q^{15} - 32 q^{16} - 16 q^{18} - 8 q^{21} - 32 q^{22} - 32 q^{25} - 16 q^{28} + 64 q^{30} + 64 q^{36} - 32 q^{37} - 16 q^{39} - 48 q^{42} - 32 q^{43} - 32 q^{46} - 16 q^{49} - 16 q^{51} - 16 q^{57} - 32 q^{58} - 16 q^{60} - 16 q^{63} - 224 q^{64} - 160 q^{67} - 16 q^{70} - 16 q^{72} - 16 q^{78} - 32 q^{79} - 16 q^{81} - 120 q^{84} - 32 q^{85} - 32 q^{88} - 16 q^{91} - 64 q^{93} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1344, [\chi])\) into newform subspaces

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