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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

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

Display 100 coefficients 10 coefficients

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 available 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

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