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Properties

Label 177.3.h
Level $177$
Weight $3$
Character orbit 177.h
Rep. character $\chi_{177}(5,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $1064$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 177.h (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 177 \)
Character field: \(\Q(\zeta_{58})\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(177, [\chi])\).

Total New Old
Modular forms 1176 1176 0
Cusp forms 1064 1064 0
Eisenstein series 112 112 0

Trace form

\( 1064 q - 29 q^{3} + 18 q^{4} - 21 q^{6} - 46 q^{7} - 49 q^{9} + O(q^{10}) \) \( 1064 q - 29 q^{3} + 18 q^{4} - 21 q^{6} - 46 q^{7} - 49 q^{9} - 94 q^{10} - 29 q^{12} - 54 q^{13} - 12 q^{15} - 158 q^{16} - 27 q^{18} - 30 q^{19} - 18 q^{21} - 142 q^{22} - 23 q^{24} + 108 q^{25} - 32 q^{27} - 70 q^{28} - 131 q^{30} - 18 q^{31} + 17 q^{33} + 90 q^{34} + 67 q^{36} - 170 q^{37} - 91 q^{39} - 2 q^{40} - 43 q^{42} - 222 q^{43} - 461 q^{45} - 54 q^{46} - 1645 q^{48} - 300 q^{49} - 893 q^{51} - 66 q^{52} - 859 q^{54} + 170 q^{55} - 27 q^{57} - 36 q^{58} + 510 q^{60} - 70 q^{61} + 610 q^{63} - 106 q^{64} + 1619 q^{66} - 182 q^{67} + 1487 q^{69} - 206 q^{70} + 2241 q^{72} + 134 q^{73} + 542 q^{75} + 246 q^{76} - 273 q^{78} - 122 q^{79} + 127 q^{81} + 122 q^{82} - 329 q^{84} - 6 q^{85} + 54 q^{87} + 38 q^{88} + 347 q^{90} + 274 q^{91} - 483 q^{93} - 826 q^{94} + 693 q^{96} - 474 q^{97} - 523 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
177.3.h.a 177.h 177.h $1064$ $4.823$ None \(0\) \(-29\) \(0\) \(-46\) $\mathrm{SU}(2)[C_{58}]$