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Properties

Label 277.2.h
Level $277$
Weight $2$
Character orbit 277.h
Rep. character $\chi_{277}(4,\cdot)$
Character field $\Q(\zeta_{46})$
Dimension $484$
Newform subspaces $1$
Sturm bound $46$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 277 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 277.h (of order \(46\) and degree \(22\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 277 \)
Character field: \(\Q(\zeta_{46})\)
Newform subspaces: \( 1 \)
Sturm bound: \(46\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(277, [\chi])\).

Total New Old
Modular forms 528 528 0
Cusp forms 484 484 0
Eisenstein series 44 44 0

Trace form

\( 484 q - 23 q^{2} - 23 q^{3} + q^{4} - 23 q^{5} - 23 q^{6} - 27 q^{7} - 23 q^{8} - 41 q^{9} + O(q^{10}) \) \( 484 q - 23 q^{2} - 23 q^{3} + q^{4} - 23 q^{5} - 23 q^{6} - 27 q^{7} - 23 q^{8} - 41 q^{9} - 23 q^{10} - 23 q^{11} - 25 q^{12} + 12 q^{13} - 23 q^{14} - 23 q^{15} - 35 q^{16} - 23 q^{17} - 23 q^{18} - 9 q^{19} + 23 q^{20} + 58 q^{21} - 33 q^{22} + 49 q^{23} + 138 q^{24} - 5 q^{25} - 23 q^{26} - 161 q^{27} + 5 q^{28} + 69 q^{29} - 19 q^{30} - 23 q^{31} - 161 q^{32} - 23 q^{33} - 33 q^{34} + 19 q^{36} + 23 q^{37} + 69 q^{38} - 41 q^{39} - 43 q^{40} - 5 q^{41} - 23 q^{42} - 23 q^{43} - 184 q^{44} + 115 q^{45} - 184 q^{46} + 31 q^{47} + 33 q^{48} - 25 q^{49} - 23 q^{50} - 23 q^{51} + 149 q^{52} - 92 q^{53} - 23 q^{54} - 2 q^{55} - 161 q^{56} - 49 q^{57} + 184 q^{58} + 19 q^{59} + 207 q^{61} - 13 q^{62} - 94 q^{63} + 11 q^{64} - 161 q^{65} - 83 q^{66} - 45 q^{67} - 138 q^{68} - 11 q^{69} + 57 q^{70} - 57 q^{71} - 345 q^{72} - 23 q^{73} - 69 q^{74} - 27 q^{75} + 66 q^{76} - 23 q^{77} - 23 q^{78} - 115 q^{79} - 23 q^{80} - 13 q^{81} - 23 q^{82} + 35 q^{83} + 286 q^{84} - 65 q^{85} - 17 q^{86} + 43 q^{87} - 45 q^{88} - 24 q^{89} + 217 q^{90} - 185 q^{91} + 331 q^{92} + 253 q^{93} - 115 q^{94} + 207 q^{96} - 23 q^{97} + 184 q^{98} - 253 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(277, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
277.2.h.a 277.h 277.h $484$ $2.212$ None \(-23\) \(-23\) \(-23\) \(-27\) $\mathrm{SU}(2)[C_{46}]$