Properties

Label 57.2.d
Level 57
Weight 2
Character orbit d
Rep. character \(\chi_{57}(56,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 57 \)
Character field: \(\Q\)
Newforms: \( 1 \)
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 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

Trace form

\(4q \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 8q^{9} \) \(\mathstrut -\mathstrut 16q^{16} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 20q^{30} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut -\mathstrut 4q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 24q^{49} \) \(\mathstrut +\mathstrut 28q^{54} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut -\mathstrut 20q^{57} \) \(\mathstrut -\mathstrut 32q^{58} \) \(\mathstrut -\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 32q^{64} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 12q^{73} \) \(\mathstrut -\mathstrut 4q^{81} \) \(\mathstrut +\mathstrut 56q^{82} \) \(\mathstrut +\mathstrut 60q^{85} \) \(\mathstrut +\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 20q^{93} \) \(\mathstrut +\mathstrut 20q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.d.a \(4\) \(0.455\) \(\Q(\sqrt{2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}+\beta _{3}q^{5}+(-1-\beta _{3})q^{6}+\cdots\)