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Properties

Label 177.12.f
Level $177$
Weight $12$
Character orbit 177.f
Rep. character $\chi_{177}(2,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $6104$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.f (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 177 \)
Character field: \(\Q(\zeta_{58})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(177, [\chi])\).

Total New Old
Modular forms 6216 6216 0
Cusp forms 6104 6104 0
Eisenstein series 112 112 0

Trace form

\( 6104 q - 1059 q^{3} - 221238 q^{4} - 29 q^{6} - 31562 q^{7} + 344741 q^{9} + O(q^{10}) \) \( 6104 q - 1059 q^{3} - 221238 q^{4} - 29 q^{6} - 31562 q^{7} + 344741 q^{9} - 58 q^{10} - 5105313 q^{12} - 58 q^{13} - 9323006 q^{15} - 217834366 q^{16} - 29 q^{18} - 25275426 q^{19} - 5361870 q^{21} - 61406286 q^{22} - 29 q^{24} + 2069374596 q^{25} - 174802842 q^{27} - 219801574 q^{28} - 29 q^{30} - 58 q^{31} - 29 q^{33} - 58 q^{34} - 1448861 q^{36} - 58 q^{37} - 29 q^{39} - 58 q^{40} - 29 q^{42} - 58 q^{43} + 7578090023 q^{45} + 2361435674 q^{46} + 49979586315 q^{48} - 55330717280 q^{49} - 32555428405 q^{51} - 58 q^{52} + 96286810563 q^{54} - 58 q^{55} - 57029166925 q^{57} - 91102654322 q^{60} - 58 q^{61} + 133120042330 q^{63} - 195867252218 q^{64} - 245543909825 q^{66} - 58 q^{67} + 25647268095 q^{69} - 58 q^{70} + 189737306083 q^{72} - 58 q^{73} + 453627292424 q^{75} - 145806138906 q^{76} - 11189945413 q^{78} - 72628658190 q^{79} + 17095483525 q^{81} - 58 q^{82} + 306377508711 q^{84} + 44963410930 q^{85} + 231025699212 q^{87} - 88082887770 q^{88} - 29 q^{90} - 58 q^{91} - 29 q^{93} - 325240398866 q^{94} - 29 q^{96} - 58 q^{97} - 29 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

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