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Properties

Label 177.12.a
Level $177$
Weight $12$
Character orbit 177.a
Rep. character $\chi_{177}(1,\cdot)$
Character field $\Q$
Dimension $108$
Newform subspaces $4$
Sturm bound $240$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(240\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(177))\).

Total New Old
Modular forms 222 108 114
Cusp forms 218 108 110
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.
\(+\)\(+\)\(+\)\(27\)
\(+\)\(-\)\(-\)\(26\)
\(-\)\(+\)\(-\)\(27\)
\(-\)\(-\)\(+\)\(28\)
Plus space\(+\)\(55\)
Minus space\(-\)\(53\)

Trace form

\( 108q - 156q^{2} + 486q^{3} + 104568q^{4} + 10740q^{5} + 22356q^{6} + 87028q^{7} - 160452q^{8} + 6377292q^{9} + O(q^{10}) \) \( 108q - 156q^{2} + 486q^{3} + 104568q^{4} + 10740q^{5} + 22356q^{6} + 87028q^{7} - 160452q^{8} + 6377292q^{9} - 486940q^{10} + 101892q^{11} + 1492992q^{12} - 3029652q^{13} + 4504276q^{14} + 1945944q^{15} + 111651000q^{16} - 21859540q^{17} - 9211644q^{18} + 59923604q^{19} + 38595068q^{20} - 13491360q^{21} - 59413688q^{22} - 46760320q^{23} + 27585360q^{24} + 1266122380q^{25} + 20750260q^{26} + 28697814q^{27} + 466168400q^{28} + 20020088q^{29} + 231351552q^{30} - 44368444q^{31} + 106857268q^{32} - 381578040q^{33} + 538090024q^{34} + 508606880q^{35} + 6174635832q^{36} - 706232492q^{37} - 133639196q^{38} - 939567276q^{39} - 1926163820q^{40} - 1880417600q^{41} - 3469231296q^{42} + 2680026528q^{43} + 2497369692q^{44} + 634186260q^{45} - 7344063956q^{46} + 989287700q^{47} + 3567255552q^{48} + 31683014752q^{49} - 20200751756q^{50} + 3265955964q^{51} - 12928276280q^{52} - 11363025772q^{53} + 1320099444q^{54} - 8362409860q^{55} + 13823010724q^{56} - 6591680208q^{57} - 30338156124q^{58} + 13773416904q^{60} - 4843486264q^{61} - 22037091288q^{62} + 5138916372q^{63} + 157253127228q^{64} + 19209056380q^{65} - 9536266728q^{66} - 1044399152q^{67} + 6031019416q^{68} - 1862885628q^{69} - 28231252916q^{70} + 38892812796q^{71} - 9474530148q^{72} - 18483896344q^{73} - 157562953072q^{74} + 3595680234q^{75} + 216257239104q^{76} - 56332492476q^{77} + 22243859388q^{78} + 59156172240q^{79} + 55375832704q^{80} + 376572715308q^{81} - 123584377260q^{82} - 56144925636q^{83} + 20382052680q^{84} - 76890444428q^{85} + 157452181448q^{86} + 17348662296q^{87} - 53332350660q^{88} + 168669818544q^{89} - 28753320060q^{90} - 38661935048q^{91} - 403687180940q^{92} - 89545314348q^{93} + 430713325488q^{94} - 251334642468q^{95} - 217187312364q^{96} - 135958957788q^{97} - 92665048472q^{98} + 6016620708q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(177))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 59
177.12.a.a \(26\) \(135.997\) None \(-78\) \(-6318\) \(3808\) \(-98819\) \(+\) \(-\)
177.12.a.b \(27\) \(135.997\) None \(-128\) \(6561\) \(-17188\) \(-126579\) \(-\) \(+\)
177.12.a.c \(27\) \(135.997\) None \(-46\) \(-6561\) \(-2442\) \(170093\) \(+\) \(+\)
177.12.a.d \(28\) \(135.997\) None \(96\) \(6804\) \(26562\) \(142333\) \(-\) \(-\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(177))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(177)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 2}\)