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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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(177))\) 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
177.12.a.a 177.a 1.a $26$ $135.997$ None \(-78\) \(-6318\) \(3808\) \(-98819\) $+$ $-$ $\mathrm{SU}(2)$
177.12.a.b 177.a 1.a $27$ $135.997$ None \(-128\) \(6561\) \(-17188\) \(-126579\) $-$ $+$ $\mathrm{SU}(2)$
177.12.a.c 177.a 1.a $27$ $135.997$ None \(-46\) \(-6561\) \(-2442\) \(170093\) $+$ $+$ $\mathrm{SU}(2)$
177.12.a.d 177.a 1.a $28$ $135.997$ None \(96\) \(6804\) \(26562\) \(142333\) $-$ $-$ $\mathrm{SU}(2)$

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

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