Properties

Label 55.2.e
Level 55
Weight 2
Character orbit e
Rep. character \(\chi_{55}(32,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 8
Newforms 2
Sturm bound 12
Trace bound 3

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Defining parameters

Level: \( N \) = \( 55 = 5 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 55.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 55 \)
Character field: \(\Q(i)\)
Newforms: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

Trace form

\( 8q - 6q^{3} - 8q^{5} + O(q^{10}) \) \( 8q - 6q^{3} - 8q^{5} + 4q^{11} + 8q^{12} - 4q^{15} - 12q^{16} + 24q^{20} - 20q^{22} + 14q^{23} + 14q^{25} - 40q^{26} + 6q^{27} + 8q^{31} - 26q^{33} + 36q^{36} - 2q^{37} + 40q^{38} - 22q^{45} - 12q^{47} + 4q^{48} - 16q^{53} + 14q^{55} - 40q^{58} - 64q^{60} + 40q^{66} + 38q^{67} - 44q^{71} + 36q^{75} + 40q^{78} - 8q^{80} + 12q^{81} + 40q^{82} - 20q^{88} + 48q^{92} + 58q^{93} - 62q^{97} + O(q^{100}) \)

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.e.a \(4\) \(0.439\) \(\Q(i, \sqrt{10})\) None \(0\) \(-4\) \(-8\) \(0\) \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+3\beta _{2}q^{4}+\cdots\)
55.2.e.b \(4\) \(0.439\) \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) \(0\) \(-2\) \(0\) \(0\) \(q+(-1+\beta _{1}-\beta _{3})q^{3}+2\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)