Properties

Label 177.6
Level 177
Weight 6
Dimension 4290
Nonzero newspaces 4
Sturm bound 13920
Trace bound 1

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Defining parameters

Level: \( N \) = \( 177 = 3 \cdot 59 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(13920\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(177))\).

Total New Old
Modular forms 5916 4406 1510
Cusp forms 5684 4290 1394
Eisenstein series 232 116 116

Trace form

\( 4290q + 12q^{2} - 47q^{3} - 66q^{4} - 12q^{5} + 79q^{6} + 22q^{7} - 336q^{8} - 191q^{9} + O(q^{10}) \) \( 4290q + 12q^{2} - 47q^{3} - 66q^{4} - 12q^{5} + 79q^{6} + 22q^{7} - 336q^{8} - 191q^{9} + 14q^{10} + 1128q^{11} - 101q^{12} - 1334q^{13} - 480q^{14} - 137q^{15} + 2214q^{16} - 1764q^{17} + 943q^{18} + 1054q^{19} - 48q^{20} + 691q^{21} - 6826q^{22} + 1680q^{23} - 3053q^{24} + 6120q^{25} + 7656q^{26} - 1487q^{27} + 262q^{28} - 9276q^{29} + 619q^{30} - 8858q^{31} - 2880q^{32} + 10123q^{33} + 10526q^{34} + 480q^{35} - 677q^{36} + 4762q^{37} - 6672q^{38} - 11513q^{39} - 2074q^{40} + 13740q^{41} - 4349q^{42} - 19346q^{43} + 4512q^{44} + 224358q^{45} + 335542q^{46} + 25106q^{47} - 344285q^{48} - 311264q^{49} - 733996q^{50} - 305325q^{51} - 380074q^{52} - 130256q^{53} + 126459q^{54} + 288764q^{55} + 1164160q^{56} + 456434q^{57} + 445880q^{58} + 401464q^{59} + 1007318q^{60} + 170406q^{61} + 183184q^{62} - 12544q^{63} - 760762q^{64} - 517302q^{65} - 917601q^{66} - 560718q^{67} - 1347088q^{68} - 639729q^{69} - 1071066q^{70} - 269324q^{71} + 192691q^{72} + 469544q^{73} + 1615960q^{74} + 755082q^{75} + 4390q^{76} - 45120q^{77} + 68875q^{78} - 43898q^{79} + 13632q^{80} - 13151q^{81} - 82498q^{82} - 164904q^{83} + 2851q^{84} - 10642q^{85} + 115728q^{86} - 83513q^{87} + 189446q^{88} + 188172q^{89} + 5803q^{90} + 50982q^{91} + 6720q^{92} - 79229q^{93} - 224122q^{94} + 6672q^{95} - 25949q^{96} - 98942q^{97} + 5697150q^{98} + 91339q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(177))\)

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
177.6.a \(\chi_{177}(1, \cdot)\) 177.6.a.a 11 1
177.6.a.b 12
177.6.a.c 12
177.6.a.d 13
177.6.d \(\chi_{177}(176, \cdot)\) 177.6.d.a 6 1
177.6.d.b 92
177.6.e \(\chi_{177}(4, \cdot)\) n/a 1400 28
177.6.f \(\chi_{177}(2, \cdot)\) n/a 2744 28

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(177))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(177)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)