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Properties

Label 3192.2.gw
Level $3192$
Weight $2$
Character orbit 3192.gw
Rep. character $\chi_{3192}(947,\cdot)$
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.gw (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

\( 3792 q - 6 q^{3} - 6 q^{4} - 12 q^{6} - 6 q^{9} + O(q^{10}) \) \( 3792 q - 6 q^{3} - 6 q^{4} - 12 q^{6} - 6 q^{9} - 6 q^{10} - 6 q^{12} - 6 q^{16} - 6 q^{18} - 12 q^{19} - 12 q^{22} + 6 q^{24} - 12 q^{25} - 12 q^{27} - 36 q^{28} + 3 q^{30} + 66 q^{33} - 24 q^{34} - 72 q^{36} + 54 q^{40} + 39 q^{42} - 48 q^{43} - 12 q^{46} - 45 q^{48} - 12 q^{49} - 6 q^{51} - 6 q^{52} + 51 q^{54} - 24 q^{57} + 24 q^{58} - 54 q^{60} - 12 q^{64} - 45 q^{66} - 12 q^{67} - 18 q^{70} - 9 q^{72} + 12 q^{73} - 12 q^{75} - 96 q^{76} - 21 q^{78} - 6 q^{81} + 138 q^{82} + 81 q^{84} + 102 q^{88} - 42 q^{90} - 108 q^{91} - 12 q^{94} + 45 q^{96} - 48 q^{97} + 30 q^{99} + O(q^{100}) \)

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.