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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
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.j (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 57 \)
Character field: \(\Q(\zeta_{18})\)
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 54 0
Cusp forms 30 30 0
Eisenstein series 24 24 0

Trace form

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

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.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 \(0\) \(-9\) \(0\) \(-6\)