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Properties

Label 3144.2.x
Level $3144$
Weight $2$
Character orbit 3144.x
Rep. character $\chi_{3144}(323,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $2096$
Sturm bound $1056$

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Defining parameters

Level: \( N \) \(=\) \( 3144 = 2^{3} \cdot 3 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3144.x (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3144 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1056\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3144, [\chi])\).

Total New Old
Modular forms 2128 2128 0
Cusp forms 2096 2096 0
Eisenstein series 32 32 0

Trace form

\( 2096 q - 6 q^{3} - 6 q^{4} - 13 q^{6} - 6 q^{9} + O(q^{10}) \) \( 2096 q - 6 q^{3} - 6 q^{4} - 13 q^{6} - 6 q^{9} + 2 q^{10} + 27 q^{12} - 6 q^{16} + 36 q^{18} - 32 q^{19} - 2 q^{22} - 74 q^{24} - 520 q^{25} + 30 q^{27} - 24 q^{28} - 6 q^{33} - 8 q^{34} + 7 q^{36} - 10 q^{40} + 28 q^{42} - 12 q^{43} + 2 q^{46} - 17 q^{48} + 488 q^{49} + 12 q^{51} - 8 q^{52} - 21 q^{54} - 12 q^{57} - 18 q^{58} + 22 q^{60} - 72 q^{64} + 11 q^{66} - 12 q^{67} - 86 q^{70} - 39 q^{72} - 12 q^{73} + 110 q^{75} + 54 q^{76} - 21 q^{78} + 2 q^{81} - 50 q^{82} - 50 q^{84} - 38 q^{88} - 131 q^{90} - 20 q^{91} - 60 q^{94} + 23 q^{96} - 36 q^{97} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3144, [\chi])\) into newform subspaces

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