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Properties

Label 3192.2.gm
Level $3192$
Weight $2$
Character orbit 3192.gm
Rep. character $\chi_{3192}(1213,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1920$
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.gm (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1064 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1280\)

Dimensions

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

Total New Old
Modular forms 3888 1920 1968
Cusp forms 3792 1920 1872
Eisenstein series 96 0 96

Trace form

\( 1920 q + O(q^{10}) \) \( 1920 q - 36 q^{10} + 18 q^{14} + 18 q^{28} - 144 q^{31} - 30 q^{32} + 102 q^{38} + 60 q^{46} - 72 q^{47} - 18 q^{50} - 36 q^{58} - 42 q^{62} - 84 q^{68} + 36 q^{70} - 18 q^{72} + 24 q^{73} + 72 q^{76} - 36 q^{78} + 96 q^{82} + 72 q^{84} - 42 q^{86} - 18 q^{90} - 12 q^{98} + O(q^{100}) \)

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

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