Properties

Label 3192.2.fk
Level $3192$
Weight $2$
Character orbit 3192.fk
Rep. character $\chi_{3192}(601,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
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.fk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
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 160 1152
Cusp forms 1248 160 1088
Eisenstein series 64 0 64

Trace form

\( 160 q + 4 q^{7} - 80 q^{9} + O(q^{10}) \) \( 160 q + 4 q^{7} - 80 q^{9} + 16 q^{11} + 6 q^{21} + 24 q^{23} + 76 q^{25} + 24 q^{29} + 8 q^{35} - 8 q^{39} + 20 q^{43} - 28 q^{49} + 72 q^{53} + 12 q^{57} - 2 q^{63} - 12 q^{67} + 8 q^{77} + 108 q^{79} - 80 q^{81} + 12 q^{85} - 6 q^{91} + 28 q^{93} - 16 q^{95} - 8 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3192, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(532, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1064, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1596, [\chi])\)\(^{\oplus 2}\)