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Properties

Label 77.2.m
Level $77$
Weight $2$
Character orbit 77.m
Rep. character $\chi_{77}(4,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $48$
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.m (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{15})\)
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 80 80 0
Cusp forms 48 48 0
Eisenstein series 32 32 0

Trace form

\( 48 q - 5 q^{2} - 3 q^{3} - q^{4} - q^{5} - 12 q^{6} - 7 q^{7} - 28 q^{8} + 5 q^{9} + O(q^{10}) \) \( 48 q - 5 q^{2} - 3 q^{3} - q^{4} - q^{5} - 12 q^{6} - 7 q^{7} - 28 q^{8} + 5 q^{9} + 4 q^{10} - 5 q^{11} - 16 q^{12} - 4 q^{13} - 24 q^{15} + q^{16} - 11 q^{17} + 18 q^{18} - 7 q^{19} - 40 q^{20} - 18 q^{21} + 40 q^{22} + 2 q^{23} - 7 q^{24} + 21 q^{25} - 15 q^{26} - 6 q^{27} + 4 q^{28} + 24 q^{29} + 21 q^{30} - 9 q^{31} - 12 q^{32} - 26 q^{33} + 72 q^{34} - 19 q^{35} + 22 q^{36} + 11 q^{37} + 3 q^{38} + 33 q^{39} + 5 q^{40} + 62 q^{41} - 60 q^{42} - 44 q^{43} + 6 q^{44} - 16 q^{45} + 16 q^{46} + 19 q^{47} + 146 q^{48} - 21 q^{49} + 6 q^{50} - q^{51} - 3 q^{52} + 21 q^{53} + 44 q^{54} + 4 q^{55} + 24 q^{56} + 20 q^{57} - 38 q^{58} + 3 q^{59} - 43 q^{60} + 18 q^{61} - 80 q^{62} + 22 q^{63} + 100 q^{64} - 10 q^{65} - 47 q^{66} - 76 q^{67} - 21 q^{68} - 126 q^{69} + 17 q^{70} + 4 q^{71} - 48 q^{72} + 26 q^{73} - 55 q^{74} - 11 q^{75} - 144 q^{76} + 32 q^{77} - 140 q^{78} + 30 q^{79} - 3 q^{80} - 57 q^{81} + 13 q^{82} - 28 q^{83} - 27 q^{84} - 98 q^{85} + 66 q^{87} + 27 q^{88} - 34 q^{89} - 18 q^{90} + 36 q^{91} - 94 q^{92} + 20 q^{93} + 45 q^{94} + 22 q^{95} - 55 q^{96} - 68 q^{97} + 120 q^{98} - 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.m.a 77.m 77.m $8$ $0.615$ \(\Q(\zeta_{15})\) None \(-2\) \(1\) \(-5\) \(-5\) $\mathrm{SU}(2)[C_{15}]$ \(q+(-1+\zeta_{15}^{4}-\zeta_{15}^{5}+\zeta_{15}^{7})q^{2}+\cdots\)
77.2.m.b 77.m 77.m $40$ $0.615$ None \(-3\) \(-4\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{15}]$