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Properties

Label 3192.2.dy
Level $3192$
Weight $2$
Character orbit 3192.dy
Rep. character $\chi_{3192}(1261,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $480$
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.dy (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
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 480 816
Cusp forms 1264 480 784
Eisenstein series 32 0 32

Trace form

\( 480 q + 4 q^{4} + 4 q^{6} + 240 q^{9} + O(q^{10}) \) \( 480 q + 4 q^{4} + 4 q^{6} + 240 q^{9} - 4 q^{10} + 16 q^{15} - 4 q^{16} + 80 q^{20} - 40 q^{22} + 8 q^{24} + 240 q^{25} + 40 q^{26} - 32 q^{31} + 20 q^{32} - 8 q^{34} - 4 q^{36} - 76 q^{38} + 76 q^{44} + 32 q^{46} + 16 q^{48} + 480 q^{49} - 16 q^{50} + 4 q^{52} - 4 q^{54} - 40 q^{58} + 28 q^{60} + 64 q^{62} + 40 q^{64} + 16 q^{66} + 8 q^{68} - 12 q^{70} + 48 q^{74} + 20 q^{76} + 8 q^{78} + 112 q^{79} + 20 q^{80} - 240 q^{81} - 24 q^{82} + 104 q^{86} + 120 q^{88} + 4 q^{90} + 84 q^{92} + 16 q^{94} + 160 q^{95} - 8 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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

Decomposition of \(S_{2}^{\mathrm{old}}(3192, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3192, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1064, [\chi])\)\(^{\oplus 2}\)