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Properties

Label 177.3.c
Level $177$
Weight $3$
Character orbit 177.c
Rep. character $\chi_{177}(58,\cdot)$
Character field $\Q$
Dimension $20$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q\)
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 42 20 22
Cusp forms 38 20 18
Eisenstein series 4 0 4

Trace form

\( 20 q - 40 q^{4} - 8 q^{7} + 60 q^{9} + O(q^{10}) \) \( 20 q - 40 q^{4} - 8 q^{7} + 60 q^{9} - 24 q^{12} + 24 q^{15} - 8 q^{16} + 16 q^{17} - 60 q^{19} - 164 q^{20} + 40 q^{22} + 100 q^{25} - 156 q^{26} + 200 q^{28} - 60 q^{29} - 32 q^{35} - 120 q^{36} + 28 q^{41} + 180 q^{46} - 96 q^{48} + 284 q^{49} - 24 q^{51} - 8 q^{53} + 24 q^{57} - 152 q^{59} - 72 q^{60} - 8 q^{62} - 24 q^{63} + 204 q^{64} - 120 q^{66} + 384 q^{68} + 92 q^{71} + 104 q^{74} + 240 q^{75} + 120 q^{76} - 468 q^{78} - 420 q^{79} + 376 q^{80} + 180 q^{81} + 168 q^{84} - 348 q^{85} + 232 q^{86} + 144 q^{87} - 212 q^{88} + 152 q^{94} + 788 q^{95} + O(q^{100}) \)

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.c.a 177.c 59.b $20$ $4.823$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(-2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(177, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(177, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 2}\)