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Properties

Label 3192.2.gp
Level $3192$
Weight $2$
Character orbit 3192.gp
Rep. character $\chi_{3192}(299,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $3792$
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.gp (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3192 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1280\)

Dimensions

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

Total New Old
Modular forms 3888 3888 0
Cusp forms 3792 3792 0
Eisenstein series 96 96 0

Trace form

\( 3792 q - 18 q^{3} - 6 q^{4} - 6 q^{9} + O(q^{10}) \) \( 3792 q - 18 q^{3} - 6 q^{4} - 6 q^{9} - 18 q^{10} - 18 q^{12} - 6 q^{16} - 36 q^{19} - 12 q^{22} + 18 q^{24} - 12 q^{25} - 36 q^{28} + 3 q^{30} - 18 q^{33} - 72 q^{36} - 18 q^{40} + 15 q^{42} - 48 q^{43} + 99 q^{48} - 12 q^{49} - 6 q^{51} - 18 q^{52} - 9 q^{54} - 24 q^{57} - 48 q^{58} - 72 q^{60} - 12 q^{64} + 45 q^{66} - 12 q^{67} + 66 q^{70} + 87 q^{72} - 108 q^{73} + 21 q^{78} - 6 q^{81} - 18 q^{82} - 9 q^{84} - 18 q^{88} - 180 q^{90} + 60 q^{91} + 135 q^{96} + 30 q^{99} + O(q^{100}) \)

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.