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Properties

Label 3192.2.gf
Level $3192$
Weight $2$
Character orbit 3192.gf
Rep. character $\chi_{3192}(289,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $480$
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.gf (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(1280\)

Dimensions

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

Total New Old
Modular forms 3936 480 3456
Cusp forms 3744 480 3264
Eisenstein series 192 0 192

Trace form

\( 480 q + O(q^{10}) \) \( 480 q - 6 q^{13} + 12 q^{17} - 6 q^{19} + 6 q^{21} + 24 q^{25} + 12 q^{27} - 24 q^{29} - 36 q^{35} - 12 q^{37} - 36 q^{41} - 54 q^{43} + 12 q^{49} + 72 q^{53} - 12 q^{57} + 24 q^{59} + 84 q^{61} + 6 q^{63} - 72 q^{65} - 6 q^{67} - 48 q^{69} + 12 q^{73} + 84 q^{75} + 36 q^{77} - 66 q^{79} - 36 q^{83} + 60 q^{85} + 72 q^{89} + 54 q^{91} - 6 q^{93} - 24 q^{97} + 12 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3192, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(532, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 3}\)