Properties

Label 77.2.f
Level $77$
Weight $2$
Character orbit 77.f
Rep. character $\chi_{77}(15,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $24$
Newform subspaces $2$
Sturm bound $16$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 77 = 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 77.f (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(77, [\chi])\).

Total New Old
Modular forms 40 24 16
Cusp forms 24 24 0
Eisenstein series 16 0 16

Trace form

\( 24 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 2 q^{5} + 6 q^{6} - 2 q^{7} - 2 q^{8} - 14 q^{9} + O(q^{10}) \) \( 24 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 2 q^{5} + 6 q^{6} - 2 q^{7} - 2 q^{8} - 14 q^{9} - 16 q^{10} + 2 q^{11} + 4 q^{12} - 2 q^{13} + 3 q^{14} - 12 q^{15} + 14 q^{16} - 16 q^{17} + 15 q^{18} + 10 q^{19} + 22 q^{20} + 12 q^{21} - 34 q^{22} + 16 q^{23} - 14 q^{24} + 12 q^{25} - 6 q^{26} - 12 q^{27} + 11 q^{28} - 6 q^{29} + 12 q^{30} - 18 q^{31} + 12 q^{32} - 16 q^{33} - 48 q^{34} - 8 q^{35} + 50 q^{36} + 10 q^{37} + 30 q^{38} + 6 q^{39} - 26 q^{40} - 32 q^{41} + 8 q^{43} - 9 q^{44} + 88 q^{45} - 13 q^{46} - 16 q^{47} - 32 q^{48} - 6 q^{49} + 18 q^{50} - 26 q^{51} + 54 q^{52} + 6 q^{53} + 64 q^{54} + 14 q^{55} - 18 q^{56} - 14 q^{57} - 19 q^{58} + 42 q^{59} - 68 q^{60} + 74 q^{62} - 10 q^{63} + 8 q^{64} + 16 q^{65} + 26 q^{66} - 68 q^{67} + 6 q^{68} + 18 q^{69} - 20 q^{70} - 28 q^{71} + 3 q^{72} - 32 q^{73} - 38 q^{74} + 14 q^{75} - 8 q^{77} - 76 q^{78} + 6 q^{79} - 120 q^{80} - 42 q^{81} + 50 q^{82} + 28 q^{83} + 12 q^{84} - 4 q^{85} - 69 q^{86} - 60 q^{87} + 48 q^{88} + 40 q^{89} - 12 q^{90} + 18 q^{91} - 89 q^{92} + 40 q^{93} - 54 q^{94} + 56 q^{95} - 32 q^{96} + 50 q^{97} + 6 q^{98} + 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(77, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
77.2.f.a 77.f 11.c $8$ $0.615$ 8.0.159390625.1 None \(-1\) \(-4\) \(3\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{4}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
77.2.f.b 77.f 11.c $16$ $0.615$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-3\) \(-2\) \(-5\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{5}-\beta _{6})q^{2}+(\beta _{9}-\beta _{11}+\beta _{13}+\cdots)q^{3}+\cdots\)