Properties

Label 57.2.d
Level $57$
Weight $2$
Character orbit 57.d
Rep. character $\chi_{57}(56,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

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