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Properties

Label 3192.2.dn
Level $3192$
Weight $2$
Character orbit 3192.dn
Rep. character $\chi_{3192}(1205,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $960$
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.dn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 456 \)
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 960 336
Cusp forms 1264 960 304
Eisenstein series 32 0 32

Trace form

\( 960 q + 4 q^{4} + O(q^{10}) \) \( 960 q + 4 q^{4} + 12 q^{10} + 4 q^{16} + 30 q^{24} - 480 q^{25} - 88 q^{30} + 84 q^{34} - 16 q^{36} + 42 q^{48} + 960 q^{49} - 48 q^{52} + 16 q^{54} - 8 q^{57} - 80 q^{58} + 42 q^{60} + 88 q^{64} - 16 q^{66} - 36 q^{70} + 42 q^{72} + 48 q^{76} + 8 q^{81} + 40 q^{82} - 112 q^{87} + 32 q^{96} + O(q^{100}) \)

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

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