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Properties

Label 3192.2.bm
Level $3192$
Weight $2$
Character orbit 3192.bm
Rep. character $\chi_{3192}(145,\cdot)$
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.bm (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

\( 160 q - 2 q^{7} - 80 q^{9} + O(q^{10}) \) \( 160 q - 2 q^{7} - 80 q^{9} + 4 q^{11} - 6 q^{13} + 12 q^{17} - 6 q^{19} + 6 q^{21} - 12 q^{23} - 152 q^{25} - 12 q^{29} + 6 q^{31} - 4 q^{35} - 18 q^{37} - 2 q^{39} - 36 q^{41} - 10 q^{43} - 10 q^{49} + 36 q^{55} + 6 q^{57} - 24 q^{59} + 36 q^{61} + 4 q^{63} + 24 q^{69} + 42 q^{73} - 4 q^{77} - 80 q^{81} + 24 q^{85} + 12 q^{91} - 44 q^{93} - 16 q^{95} - 12 q^{97} + 4 q^{99} + O(q^{100}) \)

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

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