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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
177.4.f.a \(1624\) \(10.443\) None \(0\) \(-21\) \(0\) \(-42\)