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Properties

Label 177.11.g
Level $177$
Weight $11$
Character orbit 177.g
Rep. character $\chi_{177}(10,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $2800$
Sturm bound $220$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 177.g (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
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 2800 2856
Cusp forms 5544 2800 2744
Eisenstein series 112 0 112

Trace form

\( 2800 q + 51200 q^{4} - 18392 q^{7} - 1968300 q^{9} + O(q^{10}) \) \( 2800 q + 51200 q^{4} - 18392 q^{7} - 1968300 q^{9} - 620136 q^{12} - 662904 q^{15} - 27925160 q^{16} + 2053136 q^{17} + 5169828 q^{19} + 1076324 q^{20} + 1829224 q^{22} - 215378180 q^{25} + 22082700 q^{26} + 102921320 q^{28} + 112503588 q^{29} + 76491392 q^{35} + 1007769600 q^{36} - 473464516 q^{41} + 6267875052 q^{46} - 370064882 q^{47} + 1676272320 q^{48} - 5907685096 q^{49} + 3322952704 q^{50} - 733970808 q^{51} + 12273119232 q^{52} - 743146628 q^{53} - 10772488422 q^{55} - 33545789440 q^{56} - 591502824 q^{57} + 6051872980 q^{59} - 1264196808 q^{60} + 11954793540 q^{61} + 14108823544 q^{62} - 362009736 q^{63} - 33075972108 q^{64} - 27116734722 q^{65} + 2764346616 q^{66} - 10217837844 q^{67} + 1794595648 q^{68} + 66189755904 q^{70} + 7588506936 q^{71} - 28211094150 q^{73} - 52341325032 q^{74} - 1890481680 q^{75} - 2044437240 q^{76} + 758396196 q^{78} + 3599839500 q^{79} + 23217941144 q^{80} - 38742048900 q^{81} + 13094894808 q^{84} - 23360564412 q^{85} - 12186923752 q^{86} - 7965322272 q^{87} - 32415437996 q^{88} + 22098322280 q^{94} - 7834510028 q^{95} - 162095629746 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{11}^{\mathrm{old}}(177, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(177, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 2}\)