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Properties

Label 3192.2.bk
Level $3192$
Weight $2$
Character orbit 3192.bk
Rep. character $\chi_{3192}(1171,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $640$
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.bk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1064 \)
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 640 656
Cusp forms 1264 640 624
Eisenstein series 32 0 32

Trace form

\( 640 q + 320 q^{9} + O(q^{10}) \) \( 640 q + 320 q^{9} + 18 q^{14} - 24 q^{20} - 640 q^{25} - 10 q^{26} + 8 q^{28} - 96 q^{35} - 26 q^{38} - 8 q^{49} + 30 q^{56} - 8 q^{57} + 10 q^{58} - 14 q^{62} + 12 q^{64} - 48 q^{66} + 66 q^{68} - 18 q^{72} + 8 q^{73} + 40 q^{76} + 36 q^{78} + 24 q^{80} - 320 q^{81} - 2 q^{82} - 42 q^{86} + 36 q^{88} - 18 q^{90} - 36 q^{94} - 42 q^{98} + O(q^{100}) \)

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

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