Properties

Label 3192.2.fc
Level $3192$
Weight $2$
Character orbit 3192.fc
Rep. character $\chi_{3192}(563,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1264$
Sturm bound $1280$

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Defining parameters

Level: \( N \) \(=\) \( 3192 = 2^{3} \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3192.fc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3192 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3192, [\chi])\).

Total New Old
Modular forms 1296 1296 0
Cusp forms 1264 1264 0
Eisenstein series 32 32 0

Trace form

\( 1264 q - 12 q^{3} + 2 q^{4} + 12 q^{6} - 4 q^{9} + O(q^{10}) \) \( 1264 q - 12 q^{3} + 2 q^{4} + 12 q^{6} - 4 q^{9} - 6 q^{10} + 2 q^{16} + 12 q^{18} - 12 q^{19} - 24 q^{22} + 604 q^{25} - 18 q^{28} - 15 q^{30} - 6 q^{33} - 20 q^{36} + 24 q^{40} - 8 q^{43} - 24 q^{46} + 33 q^{48} - 8 q^{49} - 12 q^{52} + 3 q^{54} - 14 q^{57} + 16 q^{58} - 64 q^{64} - 9 q^{66} - 12 q^{67} + 30 q^{70} - 30 q^{75} + 96 q^{76} - 21 q^{78} - 4 q^{81} - 21 q^{84} + 36 q^{88} + 33 q^{90} - 96 q^{91} + 36 q^{94} - 108 q^{96} - 22 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3192, [\chi])\) into newform subspaces

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