Properties

Label 55.2.l
Level 55
Weight 2
Character orbit l
Rep. character \(\chi_{55}(2,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 32
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.l (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 55 \)
Character field: \(\Q(\zeta_{20})\)
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 64 64 0
Cusp forms 32 32 0
Eisenstein series 32 32 0

Trace form

\( 32q - 10q^{2} - 4q^{3} - 2q^{5} - 20q^{6} - 10q^{8} + O(q^{10}) \) \( 32q - 10q^{2} - 4q^{3} - 2q^{5} - 20q^{6} - 10q^{8} - 24q^{11} + 12q^{12} - 10q^{13} + 14q^{15} - 8q^{16} - 10q^{18} + 16q^{20} + 10q^{22} - 24q^{23} + 16q^{25} + 20q^{26} - 16q^{27} + 50q^{28} + 30q^{30} - 28q^{31} + 66q^{33} - 10q^{35} + 24q^{36} - 8q^{37} + 10q^{38} - 50q^{40} + 40q^{41} - 10q^{42} - 28q^{45} + 60q^{46} - 28q^{47} - 54q^{48} - 50q^{50} + 20q^{51} - 50q^{52} - 24q^{53} - 64q^{55} - 80q^{56} + 30q^{57} - 50q^{58} + 34q^{60} - 60q^{61} + 100q^{62} - 30q^{63} - 100q^{66} - 8q^{67} - 30q^{68} + 30q^{70} + 24q^{71} + 80q^{72} + 50q^{73} + 34q^{75} + 70q^{77} + 60q^{78} + 98q^{80} - 12q^{81} - 10q^{82} + 90q^{83} + 30q^{85} + 100q^{86} + 170q^{88} - 20q^{90} + 20q^{91} - 68q^{92} - 8q^{93} - 40q^{95} - 8q^{97} + O(q^{100}) \)

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.l.a \(32\) \(0.439\) None \(-10\) \(-4\) \(-2\) \(0\)