Properties

Label 77.2.e
Level $77$
Weight $2$
Character orbit 77.e
Rep. character $\chi_{77}(23,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $2$
Sturm bound $16$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 77 = 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 77.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 20 12 8
Cusp forms 12 12 0
Eisenstein series 8 0 8

Trace form

\( 12q - 2q^{3} - 4q^{4} - 4q^{5} - 8q^{6} + 2q^{7} - 12q^{8} + O(q^{10}) \) \( 12q - 2q^{3} - 4q^{4} - 4q^{5} - 8q^{6} + 2q^{7} - 12q^{8} + 6q^{10} + 6q^{12} - 16q^{13} + 4q^{15} + 4q^{16} + 6q^{17} + 2q^{18} + 2q^{19} + 40q^{20} - 2q^{21} - 12q^{23} - 8q^{24} - 6q^{25} - 10q^{26} + 16q^{27} + 16q^{28} - 24q^{29} + 4q^{30} - 6q^{31} + 12q^{32} - 4q^{33} - 32q^{34} - 6q^{35} - 12q^{36} + 4q^{37} - 8q^{38} + 2q^{39} + 8q^{41} - 20q^{42} + 4q^{43} + 4q^{44} + 6q^{45} + 34q^{46} + 6q^{47} - 16q^{48} - 24q^{49} + 24q^{50} + 16q^{51} - 2q^{52} - 26q^{53} + 26q^{54} + 16q^{55} + 6q^{56} + 40q^{57} - 2q^{58} - 8q^{59} - 12q^{60} + 12q^{61} + 20q^{62} + 18q^{63} - 20q^{64} - 30q^{65} + 2q^{66} + 16q^{67} + 16q^{68} + 36q^{69} + 18q^{70} - 4q^{71} - 22q^{72} + 14q^{73} - 40q^{74} - 34q^{75} - 96q^{76} - 2q^{77} + 18q^{80} + 2q^{81} - 38q^{82} - 52q^{83} + 12q^{84} - 32q^{85} + 30q^{86} - 6q^{87} - 12q^{88} + 14q^{89} - 52q^{90} - 6q^{91} + 44q^{92} + 20q^{93} + 10q^{94} + 8q^{95} - 30q^{96} + 108q^{97} - 30q^{98} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
77.2.e.a \(6\) \(0.615\) \(\Q(\zeta_{18})\) None \(0\) \(-3\) \(-6\) \(0\) \(q+(-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots\)
77.2.e.b \(6\) \(0.615\) 6.0.1783323.2 None \(0\) \(1\) \(2\) \(2\) \(q+(-\beta _{3}+\beta _{5})q^{2}+\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)