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Properties

Label 177.4.f
Level $177$
Weight $4$
Character orbit 177.f
Rep. character $\chi_{177}(2,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $1624$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(177, [\chi])\).

Total New Old
Modular forms 1736 1736 0
Cusp forms 1624 1624 0
Eisenstein series 112 112 0

Trace form

\( 1624 q - 21 q^{3} - 278 q^{4} - 29 q^{6} - 42 q^{7} - 25 q^{9} + O(q^{10}) \) \( 1624 q - 21 q^{3} - 278 q^{4} - 29 q^{6} - 42 q^{7} - 25 q^{9} - 58 q^{10} - 57 q^{12} - 58 q^{13} - 11 q^{15} - 926 q^{16} - 29 q^{18} + 126 q^{19} + 159 q^{21} + 2 q^{22} - 29 q^{24} + 656 q^{25} - 99 q^{27} - 54 q^{28} - 29 q^{30} - 58 q^{31} - 29 q^{33} - 58 q^{34} + 859 q^{36} - 58 q^{37} - 29 q^{39} - 58 q^{40} - 29 q^{42} - 58 q^{43} + 1703 q^{45} + 602 q^{46} + 9507 q^{48} - 1192 q^{49} + 1511 q^{51} - 58 q^{52} - 7743 q^{54} - 58 q^{55} - 7441 q^{57} - 18722 q^{60} - 58 q^{61} - 3251 q^{63} - 4634 q^{64} - 1751 q^{66} - 58 q^{67} + 6003 q^{69} - 58 q^{70} + 21547 q^{72} - 58 q^{73} + 3869 q^{75} + 5622 q^{76} - 3253 q^{78} + 1446 q^{79} + 247 q^{81} - 58 q^{82} + 3303 q^{84} + 790 q^{85} - 2199 q^{87} - 5818 q^{88} - 29 q^{90} - 58 q^{91} - 29 q^{93} - 946 q^{94} - 29 q^{96} - 58 q^{97} - 29 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
177.4.f.a 177.f 177.f $1624$ $10.443$ None \(0\) \(-21\) \(0\) \(-42\) $\mathrm{SU}(2)[C_{58}]$