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 $2$

Related objects

Downloads

Learn more about

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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 59
177.4.a.a \(7\) \(10.443\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-8\) \(21\) \(-28\) \(-59\) \(-\) \(+\) \(q+(-1-\beta _{1})q^{2}+3q^{3}+(3+2\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
177.4.a.b \(7\) \(10.443\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-21\) \(-2\) \(-59\) \(+\) \(-\) \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
177.4.a.c \(8\) \(10.443\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(2\) \(-24\) \(-12\) \(53\) \(+\) \(+\) \(q+\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
177.4.a.d \(8\) \(10.443\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(6\) \(24\) \(42\) \(53\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

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

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