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Properties

Label 177.11.h
Level $177$
Weight $11$
Character orbit 177.h
Rep. character $\chi_{177}(5,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $5544$
Sturm bound $220$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 177.h (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 177 \)
Character field: \(\Q(\zeta_{58})\)
Sturm bound: \(220\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(177, [\chi])\).

Total New Old
Modular forms 5656 5656 0
Cusp forms 5544 5544 0
Eisenstein series 112 112 0

Trace form

\( 5544 q + 79 q^{3} + 100298 q^{4} + 13731 q^{6} - 18446 q^{7} + 61235 q^{9} + O(q^{10}) \) \( 5544 q + 79 q^{3} + 100298 q^{4} + 13731 q^{6} - 18446 q^{7} + 61235 q^{9} - 347614 q^{10} + 32803 q^{12} - 54 q^{13} - 2630742 q^{15} - 49123598 q^{16} - 4676739 q^{18} + 5152962 q^{19} + 6460920 q^{21} - 3200206 q^{22} + 9615961 q^{24} + 372865028 q^{25} - 10979438 q^{27} - 9967430 q^{28} - 68506811 q^{30} + 17892726 q^{31} - 114680011 q^{33} + 76288858 q^{34} + 28561027 q^{36} + 45384734 q^{37} - 74202199 q^{39} + 251902158 q^{40} + 370387661 q^{42} - 118977534 q^{43} - 2244604061 q^{45} - 357934982 q^{46} - 8644223137 q^{48} - 8484693980 q^{49} + 4620433459 q^{51} - 614376114 q^{52} - 3824195599 q^{54} + 832675010 q^{55} - 7746681399 q^{57} - 854083300 q^{58} + 35163794190 q^{60} + 859336666 q^{61} + 3896470324 q^{63} + 28617175878 q^{64} - 35694178741 q^{66} - 3089051110 q^{67} + 24100357415 q^{69} - 5638573086 q^{70} - 14841615387 q^{72} + 3509503150 q^{73} + 35962362212 q^{75} - 4604748138 q^{76} - 17856145665 q^{78} + 8477671934 q^{79} + 4552558675 q^{81} + 27579055898 q^{82} + 1342753279 q^{84} - 7992092366 q^{85} + 6884794584 q^{87} - 19995031882 q^{88} - 3386697013 q^{90} + 23659516330 q^{91} + 5199828753 q^{93} - 2290652650 q^{94} + 12439555629 q^{96} + 17322740430 q^{97} - 9730745311 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

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