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Properties

Label 177.14.e
Level $177$
Weight $14$
Character orbit 177.e
Rep. character $\chi_{177}(4,\cdot)$
Character field $\Q(\zeta_{29})$
Dimension $3640$
Sturm bound $280$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.e (of order \(29\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q(\zeta_{29})\)
Sturm bound: \(280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(177, [\chi])\).

Total New Old
Modular forms 7336 3640 3696
Cusp forms 7224 3640 3584
Eisenstein series 112 0 112

Trace form

\( 3640 q - 532480 q^{4} - 93312 q^{6} - 162964 q^{7} + 2153748 q^{8} - 69087330 q^{9} + O(q^{10}) \) \( 3640 q - 532480 q^{4} - 93312 q^{6} - 162964 q^{7} + 2153748 q^{8} - 69087330 q^{9} - 9185164 q^{10} + 12689652 q^{11} - 23730408 q^{12} - 35473832 q^{13} + 164304908 q^{14} - 36009684 q^{15} - 2125311256 q^{16} - 139949264 q^{17} + 497721012 q^{19} - 960319052 q^{20} + 488861416 q^{22} - 405938000 q^{23} - 1146617856 q^{24} - 27751607430 q^{25} + 1781673668 q^{26} - 5003519280 q^{28} - 3222241244 q^{29} - 2299073544 q^{30} - 1660838388 q^{31} - 4986609364 q^{32} - 17023864608 q^{33} - 43592951264 q^{34} - 2024455328 q^{35} - 282981703680 q^{36} - 92942704 q^{37} - 33140219380 q^{38} - 59393122992 q^{39} - 891049364 q^{40} + 35046712052 q^{41} - 16454264832 q^{42} - 11954058584 q^{43} - 105497072124 q^{44} + 225119657268 q^{46} + 1036544326806 q^{47} + 247151365344 q^{48} - 3906818264778 q^{49} + 106366110376 q^{50} + 9387152208 q^{51} + 3538140259464 q^{52} - 501267002092 q^{53} - 49589822592 q^{54} - 4156302514990 q^{55} - 1230291819972 q^{56} + 239908365432 q^{57} + 4205192095988 q^{58} + 4205526809272 q^{59} + 494226640584 q^{60} - 5987225098504 q^{61} - 6408829718792 q^{62} - 86605751124 q^{63} + 5793639423940 q^{64} + 14397529439474 q^{65} + 1412127418392 q^{66} + 4844029225276 q^{67} - 15063120089960 q^{68} - 361008495324 q^{69} - 24919573209484 q^{70} + 6646230576712 q^{71} + 1144589990868 q^{72} + 2528825276950 q^{73} - 51201761967640 q^{74} + 3202403711328 q^{75} + 10686507607936 q^{76} + 2589274629108 q^{77} + 966308229468 q^{78} + 1709020849120 q^{79} + 738136225376 q^{80} - 36715839742530 q^{81} - 8610854598060 q^{82} - 5660596714452 q^{83} - 5137864541640 q^{84} - 20521229667140 q^{85} + 20589316643368 q^{86} + 2780620334748 q^{87} + 23985412643844 q^{88} + 3028883239716 q^{89} - 4881372741324 q^{90} + 34367888495208 q^{91} - 25896491902420 q^{92} - 8437781512044 q^{93} - 7962363895632 q^{94} - 12880518979212 q^{95} - 28526415103764 q^{96} + 3496580195080 q^{97} - 352197019601266 q^{98} + 6743801348532 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

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

Decomposition of \(S_{14}^{\mathrm{old}}(177, [\chi])\) into lower level spaces

\( S_{14}^{\mathrm{old}}(177, [\chi]) \cong \) \(S_{14}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 2}\)