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Properties

Label 177.10.a
Level $177$
Weight $10$
Character orbit 177.a
Rep. character $\chi_{177}(1,\cdot)$
Character field $\Q$
Dimension $86$
Newform subspaces $4$
Sturm bound $200$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(200\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(177))\).

Total New Old
Modular forms 182 86 96
Cusp forms 178 86 92
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.
\(+\)\(+\)\(+\)\(21\)
\(+\)\(-\)\(-\)\(22\)
\(-\)\(+\)\(-\)\(22\)
\(-\)\(-\)\(+\)\(21\)
Plus space\(+\)\(42\)
Minus space\(-\)\(44\)

Trace form

\( 86q + 36q^{2} + 21848q^{4} + 5688q^{5} - 6156q^{6} - 19052q^{7} + 43356q^{8} + 564246q^{9} + O(q^{10}) \) \( 86q + 36q^{2} + 21848q^{4} + 5688q^{5} - 6156q^{6} - 19052q^{7} + 43356q^{8} + 564246q^{9} + 27556q^{10} - 146784q^{11} + 41472q^{12} + 260412q^{13} + 48020q^{14} - 3564q^{15} + 5839992q^{16} + 762880q^{17} + 236196q^{18} - 802976q^{19} + 2574364q^{20} - 2204496q^{21} + 794696q^{22} + 7856416q^{23} + 2445552q^{24} + 30671818q^{25} + 957428q^{26} - 14922192q^{28} + 11771824q^{29} - 3742848q^{30} - 19158464q^{31} - 35537452q^{32} + 5409504q^{33} - 1011864q^{34} - 39011792q^{35} + 143344728q^{36} - 8086716q^{37} + 15353156q^{38} - 15340752q^{39} - 62318732q^{40} + 2065304q^{41} - 9675936q^{42} + 40352256q^{43} - 263092068q^{44} + 37318968q^{45} + 74567340q^{46} - 48018944q^{47} + 31850496q^{48} + 465333642q^{49} - 54115852q^{50} + 1422360q^{51} + 10875464q^{52} - 126444392q^{53} - 40389516q^{54} + 355921192q^{55} + 273207812q^{56} + 53163216q^{57} + 125257412q^{58} - 300832056q^{60} - 66138036q^{61} + 803947080q^{62} - 125000172q^{63} + 960564412q^{64} - 237087616q^{65} + 52453656q^{66} - 347567712q^{67} + 237334040q^{68} + 541860192q^{69} + 114199756q^{70} - 429231336q^{71} + 284458716q^{72} + 303742116q^{73} - 1362650768q^{74} + 539186544q^{75} + 406156320q^{76} - 1337710440q^{77} + 656900604q^{78} - 50048060q^{79} + 2204062496q^{80} + 3702018006q^{81} - 2080039788q^{82} + 2141112288q^{83} - 1147819896q^{84} - 1146465264q^{85} - 3527267000q^{86} - 1207230156q^{87} + 2055794748q^{88} + 387532320q^{89} + 180794916q^{90} + 1453410968q^{91} + 4085941460q^{92} + 1276818228q^{93} - 1740248112q^{94} - 104151696q^{95} + 846196308q^{96} + 3435957252q^{97} - 3840059704q^{98} - 963049824q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(177))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 59
177.10.a.a \(21\) \(91.161\) None \(-66\) \(1701\) \(-2964\) \(-30775\) \(-\) \(-\)
177.10.a.b \(21\) \(91.161\) None \(20\) \(-1701\) \(2058\) \(-17167\) \(+\) \(+\)
177.10.a.c \(22\) \(91.161\) None \(36\) \(-1782\) \(808\) \(21249\) \(+\) \(-\)
177.10.a.d \(22\) \(91.161\) None \(46\) \(1782\) \(5786\) \(7641\) \(-\) \(+\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(177))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(177)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 2}\)