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Properties

Label 3192.2.gb
Level $3192$
Weight $2$
Character orbit 3192.gb
Rep. character $\chi_{3192}(353,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
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.gb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 399 \)
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 320 992
Cusp forms 1248 320 928
Eisenstein series 64 0 64

Trace form

\( 320 q - 2 q^{7} + O(q^{10}) \) \( 320 q - 2 q^{7} + 6 q^{13} + 4 q^{15} - 6 q^{19} + 312 q^{25} + 42 q^{31} - 10 q^{37} - 2 q^{39} + 14 q^{43} + 24 q^{45} + 10 q^{49} + 28 q^{57} + 12 q^{63} + 4 q^{67} - 42 q^{73} - 54 q^{75} + 28 q^{79} + 24 q^{81} - 4 q^{85} + 32 q^{91} + 24 q^{93} - 12 q^{97} - 32 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3192, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1596, [\chi])\)\(^{\oplus 2}\)