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Properties

Label 177.10.f
Level $177$
Weight $10$
Character orbit 177.f
Rep. character $\chi_{177}(2,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $4984$
Sturm bound $200$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.f (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 177 \)
Character field: \(\Q(\zeta_{58})\)
Sturm bound: \(200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(177, [\chi])\).

Total New Old
Modular forms 5096 5096 0
Cusp forms 4984 4984 0
Eisenstein series 112 112 0

Trace form

\( 4984 q + 267 q^{3} - 45110 q^{4} - 29 q^{6} + 9702 q^{7} - 61765 q^{9} + O(q^{10}) \) \( 4984 q + 267 q^{3} - 45110 q^{4} - 29 q^{6} + 9702 q^{7} - 61765 q^{9} - 58 q^{10} + 258207 q^{12} - 58 q^{13} + 451717 q^{15} - 11927486 q^{16} - 29 q^{18} + 787806 q^{19} - 288633 q^{21} - 389326 q^{22} - 29 q^{24} + 68185280 q^{25} + 7765317 q^{27} + 15050394 q^{28} - 29 q^{30} - 58 q^{31} - 29 q^{33} - 58 q^{34} - 58306397 q^{36} - 58 q^{37} - 29 q^{39} - 58 q^{40} - 29 q^{42} - 58 q^{43} + 434052767 q^{45} - 53909734 q^{46} + 805730763 q^{48} - 891969640 q^{49} - 6409657 q^{51} - 58 q^{52} - 1416228717 q^{54} - 58 q^{55} + 842724551 q^{57} + 2365886878 q^{60} - 58 q^{61} - 2763934211 q^{63} - 3893702906 q^{64} - 768635393 q^{66} - 58 q^{67} + 3416566995 q^{69} - 58 q^{70} - 6361640477 q^{72} - 58 q^{73} + 3821534261 q^{75} + 790959942 q^{76} + 1481293787 q^{78} + 402953526 q^{79} - 57386309 q^{81} - 58 q^{82} - 2950382457 q^{84} + 43196854 q^{85} - 955520103 q^{87} - 1462623322 q^{88} - 29 q^{90} - 58 q^{91} - 29 q^{93} + 1048869518 q^{94} - 29 q^{96} - 58 q^{97} - 29 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

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