Properties

Label 177.12
Level 177
Weight 12
Dimension 9510
Nonzero newspaces 4
Sturm bound 27840
Trace bound 1

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Defining parameters

Level: \( N \) = \( 177 = 3 \cdot 59 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(27840\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(177))\).

Total New Old
Modular forms 12876 9626 3250
Cusp forms 12644 9510 3134
Eisenstein series 232 116 116

Trace form

\( 9510q - 156q^{2} + 457q^{3} - 8130q^{4} + 10740q^{5} + 37879q^{6} + 55462q^{7} - 310128q^{8} - 118127q^{9} + O(q^{10}) \) \( 9510q - 156q^{2} + 457q^{3} - 8130q^{4} + 10740q^{5} + 37879q^{6} + 55462q^{7} - 310128q^{8} - 118127q^{9} + 837662q^{10} - 1275672q^{11} + 1961467q^{12} - 1532486q^{13} + 4330560q^{14} - 2609849q^{15} - 7658586q^{16} - 6168708q^{17} - 9211673q^{18} + 39022750q^{19} + 43346640q^{20} - 13491389q^{21} - 99502474q^{22} - 30624720q^{23} + 75361075q^{24} + 39982392q^{25} - 119529384q^{26} + 28697785q^{27} + 224078662q^{28} - 21502524q^{29} - 203565989q^{30} + 101874742q^{31} + 37776960q^{32} + 309988267q^{33} - 481159282q^{34} - 298142400q^{35} - 476643557q^{36} - 1329481718q^{37} + 3043779024q^{38} + 372379975q^{39} + 1665387302q^{40} - 1797666900q^{41} - 1052326109q^{42} + 1915894318q^{43} - 5148612192q^{44} + 8940859782q^{45} - 43999234842q^{46} + 18362345642q^{47} + 56256907843q^{48} - 4972784448q^{49} - 80036056132q^{50} - 35082339309q^{51} - 6900671850q^{52} + 31440524752q^{53} + 98525240055q^{54} + 62344966628q^{55} - 16221929216q^{56} - 74695326238q^{57} - 77814581960q^{58} - 63224911400q^{59} - 50430047146q^{60} + 42706458422q^{61} + 112358888608q^{62} + 143908746716q^{63} + 268724328262q^{64} - 42274320054q^{65} - 213484718733q^{66} - 196733569918q^{67} - 294265045264q^{68} + 33089075055q^{69} + 429404858950q^{70} + 346924186372q^{71} + 171424557811q^{72} - 205962430872q^{73} - 692605299656q^{74} + 296931486942q^{75} + 157496053030q^{76} + 35412654720q^{77} + 29045640283q^{78} - 7441084778q^{79} + 41126295360q^{80} - 6973568831q^{81} - 140218018258q^{82} - 17536908072q^{83} - 54451128989q^{84} + 33125961902q^{85} + 149439761328q^{86} + 5225113303q^{87} - 197810803066q^{88} + 50945538348q^{89} + 49466528251q^{90} + 42540201222q^{91} - 123601369920q^{92} - 24755576429q^{93} + 242695649606q^{94} - 209552478960q^{95} - 9179801309q^{96} + 78184989634q^{97} + 221457251670q^{98} - 75327155957q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(177))\)

We only show spaces with even 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
177.12.a \(\chi_{177}(1, \cdot)\) 177.12.a.a 26 1
177.12.a.b 27
177.12.a.c 27
177.12.a.d 28
177.12.d \(\chi_{177}(176, \cdot)\) n/a 218 1
177.12.e \(\chi_{177}(4, \cdot)\) n/a 3080 28
177.12.f \(\chi_{177}(2, \cdot)\) n/a 6104 28

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

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(177))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(177)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)