Properties

Label 55.2.b
Level 55
Weight 2
Character orbit b
Rep. character \(\chi_{55}(34,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 55 = 5 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 55.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(55, [\chi])\).

Total New Old
Modular forms 8 4 4
Cusp forms 4 4 0
Eisenstein series 4 0 4

Trace form

\( 4q - 6q^{4} - 3q^{5} + 8q^{6} - 2q^{9} + O(q^{10}) \) \( 4q - 6q^{4} - 3q^{5} + 8q^{6} - 2q^{9} - 10q^{10} - 4q^{11} + 12q^{14} + q^{15} + 14q^{16} - 16q^{19} - 12q^{20} + 12q^{21} + 4q^{24} + q^{25} - 12q^{29} - 6q^{30} + 2q^{31} + 16q^{34} + 18q^{35} - 30q^{36} + 28q^{40} + 12q^{41} + 6q^{44} + 18q^{45} - 8q^{46} - 20q^{49} - 18q^{50} - 28q^{51} + 20q^{54} + 3q^{55} - 60q^{56} + 18q^{59} - 18q^{60} + 20q^{61} - 2q^{64} - 8q^{66} + 14q^{69} + 24q^{70} - 6q^{71} + 12q^{74} + 15q^{75} + 24q^{76} - 28q^{79} + 6q^{80} - 8q^{81} + 48q^{84} + 2q^{85} - 12q^{86} + 6q^{89} - 28q^{90} - 44q^{94} + 12q^{95} + 36q^{96} + 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(55, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
55.2.b.a \(4\) \(0.439\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(0\) \(-3\) \(0\) \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(\beta _{1}-\beta _{3})q^{3}+\cdots\)