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Properties

Label 277.2.b
Level $277$
Weight $2$
Character orbit 277.b
Rep. character $\chi_{277}(276,\cdot)$
Character field $\Q$
Dimension $22$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 277 \)
Character field: \(\Q\)
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 24 24 0
Cusp forms 22 22 0
Eisenstein series 2 2 0

Trace form

\( 22 q - 24 q^{4} + 4 q^{7} + 18 q^{9} + O(q^{10}) \) \( 22 q - 24 q^{4} + 4 q^{7} + 18 q^{9} + 2 q^{12} - 12 q^{13} + 12 q^{16} - 14 q^{19} - 12 q^{21} + 10 q^{22} + 20 q^{23} - 18 q^{25} - 28 q^{28} - 4 q^{30} + 10 q^{34} - 42 q^{36} + 18 q^{39} + 20 q^{40} - 18 q^{41} - 8 q^{47} - 56 q^{48} + 2 q^{49} + 58 q^{52} + 48 q^{55} + 26 q^{57} - 42 q^{59} - 10 q^{62} - 44 q^{63} - 34 q^{64} + 60 q^{66} + 22 q^{67} - 12 q^{69} + 58 q^{70} + 34 q^{71} + 46 q^{74} - 42 q^{75} + 26 q^{76} - 10 q^{81} - 58 q^{83} - 10 q^{84} + 42 q^{85} - 6 q^{86} - 20 q^{87} + 22 q^{88} + 24 q^{89} + 36 q^{90} + 24 q^{91} - 32 q^{92} + O(q^{100}) \)

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.b.a 277.b 277.b $22$ $2.212$ None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$