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Properties

Label 3192.2.er
Level $3192$
Weight $2$
Character orbit 3192.er
Rep. character $\chi_{3192}(2053,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $576$
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.er (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
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 1296 576 720
Cusp forms 1264 576 688
Eisenstein series 32 0 32

Trace form

\( 576 q - 4 q^{2} + 4 q^{4} + 8 q^{8} + 288 q^{9} + O(q^{10}) \) \( 576 q - 4 q^{2} + 4 q^{4} + 8 q^{8} + 288 q^{9} - 32 q^{14} + 20 q^{16} + 4 q^{18} + 32 q^{20} + 24 q^{22} + 16 q^{23} + 12 q^{24} + 288 q^{25} - 32 q^{26} + 44 q^{28} + 16 q^{30} - 4 q^{32} + 48 q^{34} + 8 q^{36} + 12 q^{40} + 8 q^{42} - 40 q^{44} - 12 q^{46} + 32 q^{48} - 128 q^{50} - 88 q^{52} + 128 q^{55} - 4 q^{56} - 16 q^{58} + 20 q^{60} - 144 q^{62} - 80 q^{64} + 44 q^{68} - 28 q^{70} + 160 q^{71} + 4 q^{72} - 20 q^{74} + 24 q^{78} - 16 q^{79} + 124 q^{80} - 288 q^{81} + 4 q^{82} + 56 q^{84} + 16 q^{86} - 48 q^{87} - 76 q^{88} - 128 q^{92} + 72 q^{94} - 20 q^{96} + 32 q^{97} + 192 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3192, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1064, [\chi])\)\(^{\oplus 2}\)