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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
55.2.g.a 55.g 11.c $8$ $0.439$ 8.0.159390625.1 None \(-4\) \(1\) \(-2\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots\)
55.2.g.b 55.g 11.c $8$ $0.439$ 8.0.13140625.1 None \(-2\) \(-5\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)