Properties

Label 57.2.e
Level 57
Weight 2
Character orbit e
Rep. character \(\chi_{57}(7,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 8
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 19 \)
Character field: \(\Q(\zeta_{3})\)
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 16 8 8
Cusp forms 8 8 0
Eisenstein series 8 0 8

Trace form

\( 8q - 2q^{3} - 4q^{4} - 2q^{5} + 2q^{6} - 12q^{8} - 4q^{9} + O(q^{10}) \) \( 8q - 2q^{3} - 4q^{4} - 2q^{5} + 2q^{6} - 12q^{8} - 4q^{9} + 4q^{10} - 4q^{11} + 12q^{12} - 4q^{13} + 2q^{14} - 2q^{15} - 4q^{16} + 4q^{17} - 4q^{19} + 44q^{20} + 2q^{21} - 16q^{22} - 10q^{23} - 32q^{26} + 4q^{27} - 16q^{28} + 4q^{29} - 8q^{30} + 24q^{31} + 12q^{32} - 2q^{33} + 4q^{34} - 18q^{35} - 4q^{36} + 42q^{38} - 12q^{39} + 24q^{40} + 16q^{41} + 4q^{42} + 4q^{43} - 14q^{44} + 4q^{45} + 32q^{46} + 24q^{47} - 6q^{48} - 16q^{49} - 56q^{50} - 4q^{51} + 2q^{53} + 2q^{54} - 12q^{55} - 48q^{56} - 6q^{57} - 32q^{58} - 10q^{59} - 22q^{60} + 26q^{62} - 16q^{64} + 12q^{65} - 20q^{66} - 20q^{67} + 8q^{68} + 36q^{69} + 24q^{70} + 12q^{71} + 6q^{72} - 8q^{73} - 4q^{74} + 20q^{75} + 20q^{76} + 20q^{77} + 26q^{78} - 12q^{79} - 10q^{80} - 4q^{81} + 4q^{82} - 8q^{83} + 36q^{84} + 18q^{86} + 24q^{87} + 24q^{88} + 22q^{89} + 4q^{90} - 12q^{91} - 2q^{92} - 18q^{93} + 2q^{95} - 44q^{96} + 20q^{98} + 2q^{99} + O(q^{100}) \)

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.e.a \(2\) \(0.455\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(2\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
57.2.e.b \(6\) \(0.455\) 6.0.954288.1 None \(1\) \(-3\) \(-2\) \(-2\) \(q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots\)