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Properties

Label 55.2.g
Level $55$
Weight $2$
Character orbit 55.g
Rep. character $\chi_{55}(16,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $16$
Newform subspaces $2$
Sturm bound $12$
Trace bound $2$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 32 16 16
Cusp forms 16 16 0
Eisenstein series 16 0 16

Trace form

\( 16q - 6q^{2} - 4q^{3} - 8q^{4} + 6q^{6} - 4q^{7} + 2q^{8} - 10q^{9} + O(q^{10}) \) \( 16q - 6q^{2} - 4q^{3} - 8q^{4} + 6q^{6} - 4q^{7} + 2q^{8} - 10q^{9} + 8q^{10} - 2q^{11} - 12q^{12} + 2q^{13} + 6q^{15} - 16q^{16} - 12q^{17} + 14q^{18} + 14q^{19} - 4q^{20} - 32q^{21} + 26q^{22} - 8q^{23} + 38q^{24} - 4q^{25} - 4q^{26} + 20q^{27} - 2q^{28} + 10q^{29} - 20q^{30} - 4q^{31} + 28q^{32} - 14q^{33} - 16q^{34} - 12q^{35} + 6q^{36} + 28q^{37} - 6q^{38} + 30q^{39} - 6q^{40} + 4q^{41} + 38q^{42} + 4q^{43} - 40q^{44} - 38q^{46} + 4q^{47} - 14q^{48} - 14q^{49} - 6q^{50} + 14q^{51} - 54q^{52} + 16q^{53} - 24q^{54} + 12q^{55} + 52q^{56} - 50q^{57} + 6q^{58} - 46q^{59} + 26q^{60} + 4q^{61} - 68q^{62} + 26q^{63} - 20q^{64} + 16q^{65} + 26q^{66} - 40q^{67} + 46q^{68} - 22q^{69} + 32q^{70} + 20q^{71} - 64q^{72} - 10q^{73} + 68q^{74} + 6q^{75} + 16q^{76} + 6q^{77} - 4q^{78} + 54q^{79} + 16q^{80} + 8q^{81} + 30q^{82} + 2q^{83} + 24q^{84} - 16q^{85} - 34q^{86} + 68q^{87} - 14q^{88} - 16q^{89} - 26q^{90} + 32q^{91} + 92q^{92} - 48q^{93} + 50q^{94} - 16q^{95} + 6q^{96} + 36q^{97} - 68q^{98} - 16q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(55, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
55.2.g.a \(8\) \(0.439\) 8.0.159390625.1 None \(-4\) \(1\) \(-2\) \(-3\) \(q+(-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots\)
55.2.g.b \(8\) \(0.439\) 8.0.13140625.1 None \(-2\) \(-5\) \(2\) \(-1\) \(q-\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)