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Properties

Label 277.2.e
Level $277$
Weight $2$
Character orbit 277.e
Rep. character $\chi_{277}(117,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $46$
Newform subspaces $3$
Sturm bound $46$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 277 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 277.e (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 277 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(46\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 50 50 0
Cusp forms 46 46 0
Eisenstein series 4 4 0

Trace form

\( 46 q - 2 q^{3} - 50 q^{4} - 6 q^{5} + 12 q^{6} + 4 q^{7} - 25 q^{9} + O(q^{10}) \) \( 46 q - 2 q^{3} - 50 q^{4} - 6 q^{5} + 12 q^{6} + 4 q^{7} - 25 q^{9} - 9 q^{10} - 6 q^{11} - 6 q^{12} - 2 q^{13} - 12 q^{14} + 62 q^{16} - 3 q^{17} - 27 q^{18} + 12 q^{19} - 33 q^{20} - 2 q^{21} + 20 q^{22} - 14 q^{23} + 36 q^{24} + 19 q^{25} + 10 q^{27} - 16 q^{28} - 6 q^{29} + 40 q^{30} - 15 q^{31} + 11 q^{34} + 3 q^{35} + 25 q^{36} + 26 q^{39} + 22 q^{40} - 42 q^{41} - 36 q^{43} + 21 q^{44} - 6 q^{45} - 42 q^{46} + 8 q^{47} + 33 q^{48} - 23 q^{49} - 60 q^{50} + 28 q^{52} - 15 q^{53} - 18 q^{55} + 30 q^{56} - 12 q^{57} - 42 q^{58} - 36 q^{59} + 7 q^{62} + 25 q^{63} - 94 q^{64} + 15 q^{65} + 42 q^{66} + 24 q^{67} + 9 q^{68} - 6 q^{69} + 41 q^{70} - q^{71} + 102 q^{72} + 32 q^{74} + 56 q^{75} - 42 q^{76} + 69 q^{77} - 126 q^{78} - 23 q^{79} + 99 q^{80} - 39 q^{81} + 31 q^{83} - 144 q^{84} - 39 q^{85} - 3 q^{86} - 76 q^{87} - 79 q^{88} + 30 q^{89} - 33 q^{90} + 37 q^{91} + 23 q^{92} + 75 q^{93} + 48 q^{94} - 9 q^{95} - 15 q^{96} - 57 q^{97} + 99 q^{98} + 42 q^{99} + O(q^{100}) \)

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.e.a 277.e 277.e $2$ $2.212$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(1+\cdots)q^{5}+\cdots\)
277.2.e.b 277.e 277.e $12$ $2.212$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-6\) \(3\) \(5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{4}-\beta _{8})q^{2}+\beta _{5}q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
277.2.e.c 277.e 277.e $32$ $2.212$ None \(0\) \(3\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$