Properties

Label 177.2.a
Level $177$
Weight $2$
Character orbit 177.a
Rep. character $\chi_{177}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $4$
Sturm bound $40$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(40\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(177))\).

Total New Old
Modular forms 22 9 13
Cusp forms 19 9 10
Eisenstein series 3 0 3

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.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(5\)

Trace form

\( 9q - 3q^{2} - q^{3} + 3q^{4} - 6q^{5} - q^{6} - 4q^{7} - 3q^{8} + 9q^{9} + O(q^{10}) \) \( 9q - 3q^{2} - q^{3} + 3q^{4} - 6q^{5} - q^{6} - 4q^{7} - 3q^{8} + 9q^{9} + 10q^{10} + q^{12} - 6q^{13} + 20q^{14} - 2q^{15} + 3q^{16} - 2q^{17} - 3q^{18} - 8q^{19} - 14q^{20} - 8q^{21} - 16q^{22} - 8q^{23} - 9q^{24} - q^{25} + 2q^{26} - q^{27} + 4q^{28} - 2q^{29} + 10q^{30} + 4q^{31} - 19q^{32} + 4q^{33} + 2q^{34} + 16q^{35} + 3q^{36} - 22q^{37} + 32q^{38} + 2q^{39} + 26q^{40} + 2q^{41} - 8q^{42} + 12q^{43} - 6q^{45} - 4q^{46} + 4q^{47} + 17q^{48} + 29q^{49} - 37q^{50} - 2q^{51} - 46q^{52} + 10q^{53} - q^{54} + 4q^{55} + 20q^{56} - 12q^{57} + 18q^{58} + q^{59} - 6q^{60} - 2q^{61} - 24q^{62} - 4q^{63} - 9q^{64} + 8q^{65} - 4q^{66} + 20q^{67} + 2q^{68} + 4q^{69} - 4q^{70} + 36q^{71} - 3q^{72} + 10q^{73} - 26q^{74} + q^{75} - 36q^{76} + 12q^{77} + 26q^{78} - 34q^{80} + 9q^{81} + 54q^{82} - 16q^{84} - 40q^{85} + 4q^{86} - 10q^{87} - 36q^{88} - 30q^{89} + 10q^{90} + 8q^{91} - 4q^{92} - 20q^{93} + 24q^{94} - 12q^{95} - 29q^{96} + 6q^{97} + 17q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(177))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 59
177.2.a.a \(2\) \(1.413\) \(\Q(\sqrt{5}) \) None \(-3\) \(2\) \(-6\) \(-7\) \(-\) \(-\) \(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}-3q^{5}+\cdots\)
177.2.a.b \(2\) \(1.413\) \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(0\) \(-7\) \(+\) \(+\) \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
177.2.a.c \(2\) \(1.413\) \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(2\) \(1\) \(-\) \(+\) \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
177.2.a.d \(3\) \(1.413\) 3.3.229.1 None \(0\) \(-3\) \(-2\) \(9\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(177))\) into lower level spaces

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