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Properties

Label 177.2.f
Level $177$
Weight $2$
Character orbit 177.f
Rep. character $\chi_{177}(2,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $504$
Newform subspaces $1$
Sturm bound $40$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 177.f (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 177 \)
Character field: \(\Q(\zeta_{58})\)
Newform subspaces: \( 1 \)
Sturm bound: \(40\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(177, [\chi])\).

Total New Old
Modular forms 616 616 0
Cusp forms 504 504 0
Eisenstein series 112 112 0

Trace form

\( 504 q - 27 q^{3} - 70 q^{4} - 29 q^{6} - 58 q^{7} - 19 q^{9} + O(q^{10}) \) \( 504 q - 27 q^{3} - 70 q^{4} - 29 q^{6} - 58 q^{7} - 19 q^{9} - 58 q^{10} - 15 q^{12} - 58 q^{13} - 38 q^{15} - 66 q^{16} - 29 q^{18} - 66 q^{19} - 24 q^{21} - 62 q^{22} - 29 q^{24} - 20 q^{25} - 54 q^{27} - 26 q^{28} - 29 q^{30} - 58 q^{31} - 29 q^{33} - 58 q^{34} + 13 q^{36} - 58 q^{37} - 29 q^{39} - 58 q^{40} - 29 q^{42} - 58 q^{43} - q^{45} - 46 q^{46} + 147 q^{48} - 48 q^{49} + 59 q^{51} - 58 q^{52} + 174 q^{54} - 58 q^{55} + 83 q^{57} + 250 q^{60} - 58 q^{61} + 82 q^{63} + 10 q^{64} + 226 q^{66} - 58 q^{67} + 87 q^{69} - 58 q^{70} + 145 q^{72} - 58 q^{73} - 28 q^{75} - 150 q^{76} - 13 q^{78} - 30 q^{79} + 13 q^{81} - 58 q^{82} - 69 q^{84} - 86 q^{85} - 36 q^{87} + 22 q^{88} - 29 q^{90} - 58 q^{91} - 29 q^{93} - 162 q^{94} - 29 q^{96} - 58 q^{97} - 29 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
177.2.f.a 177.f 177.f $504$ $1.413$ None \(0\) \(-27\) \(0\) \(-58\) $\mathrm{SU}(2)[C_{58}]$