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Properties

Label 57.2.i
Level 57
Weight 2
Character orbit i
Rep. character \(\chi_{57}(4,\cdot)\)
Character field \(\Q(\zeta_{9})\)
Dimension 18
Newforms 2
Sturm bound 13
Trace bound 1

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Defining parameters

Level: \( N \) = \( 57 = 3 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 57.i (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newforms: \( 2 \)
Sturm bound: \(13\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 54 18 36
Cusp forms 30 18 12
Eisenstein series 24 0 24

Trace form

\( 18q - 6q^{4} - 6q^{6} - 6q^{7} + O(q^{10}) \) \( 18q - 6q^{4} - 6q^{6} - 6q^{7} - 24q^{10} - 6q^{11} - 6q^{12} - 9q^{13} + 6q^{14} + 12q^{15} + 18q^{16} + 9q^{19} - 12q^{20} + 3q^{21} - 24q^{22} + 24q^{24} - 12q^{25} + 12q^{26} - 3q^{27} + 30q^{28} + 12q^{29} - 24q^{31} - 6q^{32} - 6q^{33} + 42q^{34} + 24q^{35} - 6q^{36} + 24q^{38} + 6q^{40} - 12q^{41} - 12q^{42} + 33q^{43} + 24q^{44} - 6q^{45} + 18q^{46} - 42q^{47} - 24q^{48} + 3q^{49} + 18q^{50} - 12q^{51} - 18q^{52} - 54q^{53} - 6q^{54} - 18q^{55} - 72q^{56} - 12q^{57} - 48q^{58} - 30q^{59} - 12q^{60} - 48q^{62} + 6q^{63} - 18q^{64} + 36q^{65} + 48q^{66} + 33q^{67} - 18q^{68} + 12q^{70} - 12q^{71} + 36q^{72} - 51q^{73} + 60q^{74} + 42q^{75} - 60q^{76} + 96q^{77} + 36q^{79} + 66q^{80} - 18q^{82} + 18q^{83} + 18q^{85} + 48q^{86} + 24q^{87} + 48q^{88} + 48q^{89} - 6q^{90} + 12q^{91} + 72q^{92} + 12q^{94} - 66q^{95} - 24q^{96} - 6q^{97} - 12q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(57, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
57.2.i.a \(6\) \(0.455\) \(\Q(\zeta_{18})\) None \(3\) \(0\) \(-6\) \(3\) \(q+(\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{2}-\zeta_{18}^{4}q^{3}+\cdots\)
57.2.i.b \(12\) \(0.455\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(0\) \(6\) \(-9\) \(q+(1-\beta _{1}-\beta _{2}+\beta _{5}-\beta _{9})q^{2}-\beta _{6}q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(57, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(57, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)