Properties

Label 177.11
Level 177
Weight 11
Dimension 8638
Nonzero newspaces 4
Sturm bound 25520
Trace bound 1

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Defining parameters

Level: \( N \) = \( 177 = 3 \cdot 59 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(25520\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(177))\).

Total New Old
Modular forms 11716 8750 2966
Cusp forms 11484 8638 2846
Eisenstein series 232 112 120

Trace form

\( 8638q + 79q^{3} - 1274q^{4} + 25891q^{6} - 68994q^{7} + 230335q^{9} + O(q^{10}) \) \( 8638q + 79q^{3} - 1274q^{4} + 25891q^{6} - 68994q^{7} + 230335q^{9} - 305338q^{10} + 32803q^{12} + 678558q^{13} - 2747549q^{15} + 2579398q^{16} - 1399709q^{18} + 3797790q^{19} + 1861243q^{21} - 20050618q^{22} + 34421731q^{24} - 6702878q^{25} - 18816977q^{27} - 20956602q^{28} + 8242531q^{30} + 119172414q^{31} - 180455069q^{33} - 36841018q^{34} + 70030627q^{36} + 243247326q^{37} - 18322661q^{39} - 405411898q^{40} + 446705251q^{42} - 429678882q^{43} - 1788143836q^{45} + 7768527302q^{46} - 370064882q^{47} - 9114304541q^{48} - 3990529906q^{49} + 3322952704q^{50} + 5565942671q^{51} + 12479418438q^{52} + 2524360100q^{53} - 6407582749q^{54} - 8647129120q^{55} - 33545789440q^{56} - 7228410180q^{57} + 341550604q^{58} + 6560015180q^{59} + 33059352518q^{60} + 7831618914q^{61} + 7570616576q^{62} + 2773883022q^{63} - 38699524154q^{64} - 27116734722q^{65} - 32052834589q^{66} - 17724807798q^{67} + 11792281600q^{68} + 26329983431q^{69} + 60928560326q^{70} + 22497030140q^{71} - 21023118365q^{72} - 16824980232q^{73} - 47477816320q^{74} + 39078573074q^{75} + 1154545734q^{76} - 4397431709q^{78} - 5954590530q^{79} - 12586648673q^{81} + 19498671302q^{82} + 565826659q^{84} + 3905141702q^{85} + 3073956451q^{87} - 26627143738q^{88} + 17581380451q^{90} + 11695268086q^{91} - 3217656773q^{93} - 28764311098q^{94} + 18533007331q^{96} + 6371795646q^{97} - 162095629746q^{98} + 9744572131q^{99} + O(q^{100}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(177))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
177.11.b \(\chi_{177}(119, \cdot)\) n/a 194 1
177.11.c \(\chi_{177}(58, \cdot)\) 177.11.c.a 100 1
177.11.g \(\chi_{177}(10, \cdot)\) n/a 2800 28
177.11.h \(\chi_{177}(5, \cdot)\) n/a 5544 28

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(177))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(177)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)