Properties

Label 177.9
Level 177
Weight 9
Dimension 6898
Nonzero newspaces 4
Sturm bound 20880
Trace bound 1

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Defining parameters

Level: \( N \) = \( 177 = 3 \cdot 59 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(20880\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(177))\).

Total New Old
Modular forms 9396 7010 2386
Cusp forms 9164 6898 2266
Eisenstein series 232 112 120

Trace form

\( 6898q - 209q^{3} + 934q^{4} - 6077q^{6} + 6942q^{7} + 10015q^{9} + O(q^{10}) \) \( 6898q - 209q^{3} + 934q^{4} - 6077q^{6} + 6942q^{7} + 10015q^{9} - 20218q^{10} + 44611q^{12} - 102978q^{13} + 60451q^{15} + 270022q^{16} - 544349q^{18} - 75810q^{19} + 314971q^{21} + 624902q^{22} - 48413q^{24} - 1360958q^{25} + 2084911q^{27} - 1736058q^{28} - 907229q^{30} + 1405854q^{31} - 1874909q^{33} + 6725318q^{34} - 2490941q^{36} - 5340738q^{37} - 4631429q^{39} - 161338q^{40} + 10583971q^{42} + 14104542q^{43} - 59811382q^{45} + 68355398q^{46} + 63546714q^{47} + 44113891q^{48} - 69287578q^{49} - 247486464q^{50} - 123161305q^{51} - 48686202q^{52} + 44302140q^{53} + 187313027q^{54} + 212599364q^{55} + 540407808q^{56} + 99341466q^{57} + 41388364q^{58} - 91298844q^{59} - 520083514q^{60} - 212493414q^{61} - 199245312q^{62} - 183285204q^{63} - 132517946q^{64} + 186364962q^{65} + 479569187q^{66} + 332267490q^{67} + 664151040q^{68} + 327024095q^{69} - 73674682q^{70} - 380816748q^{71} - 975168797q^{72} - 414271548q^{73} + 142718976q^{74} + 491840888q^{75} + 18786438q^{76} - 155615069q^{78} + 91923870q^{79} + 121745887q^{81} + 168416582q^{82} - 78120029q^{84} - 67253818q^{85} - 124165469q^{87} + 4999622q^{88} + 50621731q^{90} + 180109942q^{91} + 63266011q^{93} - 366476602q^{94} + 395974627q^{96} - 589084098q^{97} - 4373193330q^{98} - 168739229q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(177))\)

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
177.9.b \(\chi_{177}(119, \cdot)\) n/a 154 1
177.9.c \(\chi_{177}(58, \cdot)\) 177.9.c.a 80 1
177.9.g \(\chi_{177}(10, \cdot)\) n/a 2240 28
177.9.h \(\chi_{177}(5, \cdot)\) n/a 4424 28

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

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(177))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(177)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)