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Properties

Label 3192.2.cx
Level $3192$
Weight $2$
Character orbit 3192.cx
Rep. character $\chi_{3192}(761,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $288$
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.cx (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
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 1312 288 1024
Cusp forms 1248 288 960
Eisenstein series 64 0 64

Trace form

\( 288 q - 4 q^{7} - 4 q^{9} + O(q^{10}) \) \( 288 q - 4 q^{7} - 4 q^{9} - 28 q^{21} - 132 q^{25} + 12 q^{31} + 24 q^{33} + 30 q^{39} + 16 q^{43} + 36 q^{45} + 36 q^{49} - 12 q^{51} - 72 q^{61} + 22 q^{63} - 24 q^{67} - 28 q^{79} - 36 q^{81} - 156 q^{87} - 16 q^{91} - 8 q^{93} + 24 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3192, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 3}\)