Properties

Label 177.8.a
Level $177$
Weight $8$
Character orbit 177.a
Rep. character $\chi_{177}(1,\cdot)$
Character field $\Q$
Dimension $68$
Newform subspaces $4$
Sturm bound $160$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(160\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(177))\).

Total New Old
Modular forms 142 68 74
Cusp forms 138 68 70
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.
\(+\)\(+\)\(+\)\(17\)
\(+\)\(-\)\(-\)\(16\)
\(-\)\(+\)\(-\)\(17\)
\(-\)\(-\)\(+\)\(18\)
Plus space\(+\)\(35\)
Minus space\(-\)\(33\)

Trace form

\( 68q - 12q^{2} + 54q^{3} + 4664q^{4} - 780q^{5} - 108q^{6} + 1476q^{7} + 636q^{8} + 49572q^{9} + O(q^{10}) \) \( 68q - 12q^{2} + 54q^{3} + 4664q^{4} - 780q^{5} - 108q^{6} + 1476q^{7} + 636q^{8} + 49572q^{9} + 260q^{10} + 5316q^{11} + 10368q^{12} + 10980q^{13} - 17836q^{14} - 216q^{15} + 342072q^{16} - 24740q^{17} - 8748q^{18} - 2860q^{19} - 452q^{20} - 3456q^{21} - 176024q^{22} - 58976q^{23} - 154224q^{24} + 984900q^{25} - 651436q^{26} + 39366q^{27} - 172016q^{28} - 311120q^{29} - 157248q^{30} - 604q^{31} + 88436q^{32} + 190296q^{33} - 797944q^{34} + 639040q^{35} + 3400056q^{36} - 710260q^{37} - 1040284q^{38} - 244620q^{39} + 1802580q^{40} + 941432q^{41} + 660096q^{42} - 637056q^{43} + 581340q^{44} - 568620q^{45} - 968020q^{46} - 678428q^{47} + 1548288q^{48} + 9776792q^{49} + 5008484q^{50} + 2598588q^{51} + 1732552q^{52} - 2867372q^{53} - 78732q^{54} - 39700q^{55} - 8128156q^{56} - 722304q^{57} - 2710396q^{58} - 7106616q^{60} + 5017912q^{61} - 6064920q^{62} + 1076004q^{63} + 33042748q^{64} + 2940020q^{65} + 1999512q^{66} - 5304496q^{67} + 374168q^{68} - 4885812q^{69} - 3642996q^{70} - 4243764q^{71} + 463644q^{72} - 16338872q^{73} + 5064880q^{74} + 245754q^{75} - 12737280q^{76} + 29922972q^{77} + 9269532q^{78} + 12391120q^{79} - 29375296q^{80} + 36137988q^{81} - 2566284q^{82} + 13277628q^{83} - 20585016q^{84} - 9427828q^{85} + 32532232q^{86} + 10963080q^{87} - 20176068q^{88} + 4515288q^{89} + 189540q^{90} + 2409016q^{91} - 13373644q^{92} - 11127996q^{93} - 18354768q^{94} - 19264308q^{95} + 17514900q^{96} - 12947124q^{97} - 22197832q^{98} + 3875364q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(177))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 59
177.8.a.a \(16\) \(55.292\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-6\) \(-432\) \(-68\) \(-2343\) \(+\) \(-\) \(q-\beta _{1}q^{2}-3^{3}q^{3}+(61+\beta _{2})q^{4}+(-5+\cdots)q^{5}+\cdots\)
177.8.a.b \(17\) \(55.292\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(-32\) \(459\) \(-1072\) \(-2407\) \(-\) \(+\) \(q+(-2+\beta _{1})q^{2}+3^{3}q^{3}+(69-3\beta _{1}+\cdots)q^{4}+\cdots\)
177.8.a.c \(17\) \(55.292\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(2\) \(-459\) \(-318\) \(3145\) \(+\) \(+\) \(q+\beta _{1}q^{2}-3^{3}q^{3}+(68+\beta _{1}+\beta _{2})q^{4}+\cdots\)
177.8.a.d \(18\) \(55.292\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(24\) \(486\) \(678\) \(3081\) \(-\) \(-\) \(q+(1+\beta _{1})q^{2}+3^{3}q^{3}+(75+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(177))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(177)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 2}\)