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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

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

Display 100 coefficients 10 coefficients

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 available 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

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