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Properties

Label 177.4.a
Level $177$
Weight $4$
Character orbit 177.a
Rep. character $\chi_{177}(1,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $4$
Sturm bound $80$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(80\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(177))\).

Total New Old
Modular forms 62 30 32
Cusp forms 58 30 28
Eisenstein series 4 0 4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(59\)FrickeDim
\(+\)\(+\)$+$\(8\)
\(+\)\(-\)$-$\(7\)
\(-\)\(+\)$-$\(7\)
\(-\)\(-\)$+$\(8\)
Plus space\(+\)\(16\)
Minus space\(-\)\(14\)

Trace form

\( 30 q + 120 q^{4} - 12 q^{6} - 12 q^{7} - 84 q^{8} + 270 q^{9} + O(q^{10}) \) \( 30 q + 120 q^{4} - 12 q^{6} - 12 q^{7} - 84 q^{8} + 270 q^{9} - 100 q^{10} - 96 q^{11} - 24 q^{12} - 68 q^{13} - 140 q^{14} + 84 q^{15} + 440 q^{16} - 40 q^{17} + 96 q^{19} + 428 q^{20} + 496 q^{22} - 64 q^{23} - 144 q^{24} + 370 q^{25} + 172 q^{26} - 320 q^{28} + 104 q^{29} - 48 q^{30} - 288 q^{31} - 812 q^{32} - 96 q^{33} - 48 q^{34} - 400 q^{35} + 1080 q^{36} - 140 q^{37} + 52 q^{38} - 336 q^{39} - 940 q^{40} - 704 q^{41} + 192 q^{42} - 896 q^{43} - 612 q^{44} + 588 q^{46} - 160 q^{47} - 288 q^{48} + 2202 q^{49} + 1624 q^{50} - 456 q^{51} - 376 q^{52} - 928 q^{53} - 108 q^{54} - 1240 q^{55} + 1732 q^{56} - 384 q^{57} + 124 q^{58} - 216 q^{60} - 2132 q^{61} - 1848 q^{62} - 108 q^{63} + 1276 q^{64} - 1040 q^{65} + 2136 q^{66} + 736 q^{67} + 1864 q^{68} - 96 q^{69} + 2204 q^{70} - 3144 q^{71} - 756 q^{72} - 284 q^{73} - 2440 q^{74} + 624 q^{75} - 1472 q^{76} - 24 q^{77} - 1452 q^{78} + 2340 q^{79} + 4384 q^{80} + 2430 q^{81} - 2388 q^{82} + 1248 q^{83} + 456 q^{84} - 288 q^{85} - 40 q^{86} - 12 q^{87} + 4188 q^{88} + 3864 q^{89} - 900 q^{90} + 1080 q^{91} - 5324 q^{92} - 468 q^{93} + 1056 q^{94} + 4272 q^{95} - 1644 q^{96} - 1916 q^{97} - 572 q^{98} - 864 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(177))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 59
177.4.a.a 177.a 1.a $7$ $10.443$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-8\) \(21\) \(-28\) \(-59\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+3q^{3}+(3+2\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
177.4.a.b 177.a 1.a $7$ $10.443$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-21\) \(-2\) \(-59\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
177.4.a.c 177.a 1.a $8$ $10.443$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(2\) \(-24\) \(-12\) \(53\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
177.4.a.d 177.a 1.a $8$ $10.443$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(6\) \(24\) \(42\) \(53\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(177))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(177)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 2}\)