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Properties

Label 57.2.f
Level $57$
Weight $2$
Character orbit 57.f
Rep. character $\chi_{57}(8,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $1$
Sturm bound $13$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 57 = 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 57.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(13\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(57, [\chi])\).

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

Trace form

\( 8q + 4q^{6} - 16q^{7} - 4q^{9} + O(q^{10}) \) \( 8q + 4q^{6} - 16q^{7} - 4q^{9} - 12q^{10} + 12q^{13} + 4q^{16} - 12q^{21} + 12q^{22} + 4q^{24} - 12q^{25} + 12q^{28} - 8q^{30} + 24q^{33} + 24q^{34} + 16q^{39} - 12q^{40} - 20q^{42} - 16q^{43} + 32q^{45} + 24q^{48} - 48q^{51} - 24q^{52} - 4q^{54} + 16q^{55} - 28q^{57} - 64q^{58} - 24q^{60} + 28q^{61} + 8q^{63} - 32q^{64} - 4q^{66} + 36q^{70} - 24q^{72} + 12q^{73} + 60q^{76} + 36q^{78} + 24q^{79} + 28q^{81} + 16q^{82} + 32q^{87} + 12q^{90} - 48q^{91} - 4q^{93} + 72q^{96} + 24q^{97} - 32q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(57, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
57.2.f.a \(8\) \(0.455\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(-16\) \(q+(-\zeta_{24}+\zeta_{24}^{5}+\zeta_{24}^{7})q^{2}+(\zeta_{24}^{2}+\cdots)q^{3}+\cdots\)