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Properties

Label 57.2.j
Level 57
Weight 2
Character orbit j
Rep. character \(\chi_{57}(2,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 30
Newform subspaces 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.j (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 57 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
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 54 0
Cusp forms 30 30 0
Eisenstein series 24 24 0

Trace form

\( 30q - 9q^{3} - 18q^{4} - 9q^{6} - 6q^{7} + 3q^{9} + O(q^{10}) \) \( 30q - 9q^{3} - 18q^{4} - 9q^{6} - 6q^{7} + 3q^{9} - 6q^{10} - 9q^{12} - 9q^{13} - 9q^{15} + 30q^{16} - 9q^{19} + 3q^{21} + 24q^{22} - 21q^{24} + 12q^{25} - 18q^{28} + 42q^{30} - 18q^{31} + 21q^{33} - 42q^{34} + 63q^{36} + 30q^{40} + 105q^{42} + 15q^{43} + 6q^{45} - 54q^{46} - 33q^{48} - 15q^{49} + 3q^{51} - 60q^{52} - 87q^{54} - 90q^{55} - 6q^{57} + 24q^{58} - 66q^{60} - 48q^{61} - 45q^{63} + 42q^{64} - 57q^{66} + 33q^{67} - 36q^{69} + 18q^{70} + 24q^{72} + 141q^{73} + 12q^{76} + 9q^{78} + 42q^{79} + 3q^{81} + 126q^{82} + 99q^{84} - 6q^{85} + 15q^{87} + 54q^{88} + 24q^{90} + 114q^{91} + 87q^{93} - 18q^{96} - 78q^{97} + 12q^{99} + O(q^{100}) \)

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.j.a \(6\) \(0.455\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{18}^{2}+2\zeta_{18}^{5})q^{3}+2\zeta_{18}q^{4}+\cdots\)
57.2.j.b \(24\) \(0.455\) None \(0\) \(-9\) \(0\) \(-6\)