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Properties

Label 177.6.f
Level $177$
Weight $6$
Character orbit 177.f
Rep. character $\chi_{177}(2,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $2744$
Sturm bound $120$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 177.f (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 177 \)
Character field: \(\Q(\zeta_{58})\)
Sturm bound: \(120\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(177, [\chi])\).

Total New Old
Modular forms 2856 2856 0
Cusp forms 2744 2744 0
Eisenstein series 112 112 0

Trace form

\( 2744 q - 51 q^{3} - 1590 q^{4} - 29 q^{6} + 22 q^{7} - 31 q^{9} + O(q^{10}) \) \( 2744 q - 51 q^{3} - 1590 q^{4} - 29 q^{6} + 22 q^{7} - 31 q^{9} - 58 q^{10} + 1215 q^{12} - 58 q^{13} - 4298 q^{15} - 20926 q^{16} - 29 q^{18} - 1842 q^{19} - 3342 q^{21} + 8082 q^{22} - 29 q^{24} + 66900 q^{25} + 18378 q^{27} + 19034 q^{28} - 29 q^{30} - 58 q^{31} - 29 q^{33} - 58 q^{34} + 20803 q^{36} - 58 q^{37} - 29 q^{39} - 58 q^{40} - 29 q^{42} - 58 q^{43} + 279167 q^{45} - 51238 q^{46} - 426453 q^{48} - 275456 q^{49} - 297781 q^{51} - 58 q^{52} + 117711 q^{54} - 58 q^{55} + 340643 q^{57} + 733438 q^{60} - 58 q^{61} + 230134 q^{63} - 364922 q^{64} - 845093 q^{66} - 58 q^{67} - 654849 q^{69} - 58 q^{70} + 219907 q^{72} - 58 q^{73} + 726836 q^{75} - 111546 q^{76} - 356293 q^{78} - 180318 q^{79} - 79583 q^{81} - 58 q^{82} - 367737 q^{84} - 111086 q^{85} + 96936 q^{87} + 1242918 q^{88} - 29 q^{90} - 58 q^{91} - 29 q^{93} + 513550 q^{94} - 29 q^{96} - 58 q^{97} - 29 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.