Base field 6.6.1868969.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - x^{3} + 8x^{2} + x - 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[17, 17, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 5w + 1]$ |
| Dimension: | $20$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{20} - 32x^{18} + 431x^{16} - 3184x^{14} + 14092x^{12} - 38285x^{10} + 62634x^{8} - 57251x^{6} + 23878x^{4} - 1920x^{2} + 36\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $-\frac{8}{45}e^{19} + \frac{241}{45}e^{17} - \frac{5993}{90}e^{15} + \frac{19862}{45}e^{13} - \frac{75554}{45}e^{11} + \frac{164623}{45}e^{9} - \frac{21176}{5}e^{7} + \frac{36703}{18}e^{5} - \frac{1778}{45}e^{3} - \frac{221}{15}e$ |
| 17 | $[17, 17, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 5w + 1]$ | $-1$ |
| 23 | $[23, 23, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $-\frac{1}{6}e^{17} + 5e^{15} - \frac{371}{6}e^{13} + 407e^{11} - \frac{4604}{3}e^{9} + \frac{6621}{2}e^{7} - 3802e^{5} + \frac{11105}{6}e^{3} - 90e$ |
| 31 | $[31, 31, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 7w - 5]$ | $-\frac{29}{180}e^{19} + \frac{877}{180}e^{17} - \frac{2743}{45}e^{15} + \frac{36739}{90}e^{13} - \frac{71141}{45}e^{11} + \frac{641377}{180}e^{9} - \frac{17751}{4}e^{7} + \frac{236963}{90}e^{5} - \frac{43771}{90}e^{3} + \frac{397}{15}e$ |
| 32 | $[32, 2, w^{5} - 6w^{3} - w^{2} + 8w + 1]$ | $-\frac{1}{60}e^{19} + \frac{29}{60}e^{17} - \frac{169}{30}e^{15} + \frac{199}{6}e^{13} - \frac{1471}{15}e^{11} + \frac{1141}{12}e^{9} + \frac{4051}{20}e^{7} - \frac{8893}{15}e^{5} + \frac{2633}{6}e^{3} - \frac{146}{5}e$ |
| 43 | $[43, 43, w^{4} - 5w^{2} + 3]$ | $\phantom{-}\frac{37}{180}e^{19} - \frac{1139}{180}e^{17} + \frac{3644}{45}e^{15} - \frac{25132}{45}e^{13} + \frac{101239}{45}e^{11} - \frac{964457}{180}e^{9} + \frac{145129}{20}e^{7} - \frac{90083}{18}e^{5} + \frac{60568}{45}e^{3} - \frac{1214}{15}e$ |
| 47 | $[47, 47, -w^{4} + w^{3} + 5w^{2} - 2w - 5]$ | $-\frac{1}{5}e^{19} + \frac{181}{30}e^{17} - \frac{751}{10}e^{15} + \frac{7468}{15}e^{13} - 1889e^{11} + \frac{61127}{15}e^{9} - \frac{45667}{10}e^{7} + \frac{19117}{10}e^{5} + \frac{3563}{15}e^{3} - \frac{253}{5}e$ |
| 49 | $[49, 7, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 1]$ | $-\frac{4}{9}e^{19} + \frac{616}{45}e^{17} - \frac{1577}{9}e^{15} + \frac{54353}{45}e^{13} - \frac{218423}{45}e^{11} + \frac{516592}{45}e^{9} - \frac{76318}{5}e^{7} + \frac{450409}{45}e^{5} - \frac{102437}{45}e^{3} + \frac{1219}{15}e$ |
| 53 | $[53, 53, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 5w - 7]$ | $\phantom{-}\frac{1}{5}e^{19} - \frac{31}{5}e^{17} + \frac{801}{10}e^{15} - \frac{5597}{10}e^{13} + 2296e^{11} - \frac{28049}{5}e^{9} + \frac{39391}{5}e^{7} - \frac{57257}{10}e^{5} + \frac{16543}{10}e^{3} - \frac{387}{5}e$ |
| 59 | $[59, 59, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 3]$ | $-\frac{1}{15}e^{16} + 2e^{14} - \frac{368}{15}e^{12} + \frac{791}{5}e^{10} - \frac{8602}{15}e^{8} + \frac{5779}{5}e^{6} - \frac{5938}{5}e^{4} + \frac{7232}{15}e^{2} - \frac{79}{5}$ |
| 71 | $[71, 71, w^{5} - w^{4} - 5w^{3} + 4w^{2} + 4w - 5]$ | $-\frac{17}{60}e^{18} + \frac{523}{60}e^{16} - \frac{1669}{15}e^{14} + \frac{2287}{3}e^{12} - \frac{45362}{15}e^{10} + \frac{83477}{12}e^{8} - \frac{173723}{20}e^{6} + \frac{145013}{30}e^{4} - \frac{1618}{3}e^{2} + \frac{133}{5}$ |
| 79 | $[79, 79, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}\frac{11}{90}e^{19} - \frac{158}{45}e^{17} + \frac{1814}{45}e^{15} - \frac{20741}{90}e^{13} + \frac{5663}{9}e^{11} - \frac{29149}{90}e^{9} - \frac{11863}{5}e^{7} + \frac{243142}{45}e^{5} - \frac{328471}{90}e^{3} + \frac{2743}{15}e$ |
| 83 | $[83, 83, w^{5} - 6w^{3} - w^{2} + 7w - 1]$ | $-\frac{1}{5}e^{19} + \frac{31}{5}e^{17} - \frac{801}{10}e^{15} + \frac{5597}{10}e^{13} - 2296e^{11} + \frac{28049}{5}e^{9} - \frac{39391}{5}e^{7} + \frac{57257}{10}e^{5} - \frac{16543}{10}e^{3} + \frac{377}{5}e$ |
| 83 | $[83, 83, 2w^{5} - w^{4} - 11w^{3} + 2w^{2} + 12w + 1]$ | $\phantom{-}\frac{1}{2}e^{18} - \frac{151}{10}e^{16} + \frac{377}{2}e^{14} - \frac{6289}{5}e^{12} + \frac{24204}{5}e^{10} - \frac{107847}{10}e^{8} + \frac{131107}{10}e^{6} - \frac{73049}{10}e^{4} + \frac{5061}{5}e^{2} - \frac{171}{5}$ |
| 89 | $[89, 89, -w^{5} + w^{4} + 4w^{3} - 2w^{2} - w - 1]$ | $-\frac{11}{30}e^{18} + \frac{111}{10}e^{16} - \frac{2084}{15}e^{14} + \frac{4647}{5}e^{12} - \frac{53728}{15}e^{10} + \frac{79601}{10}e^{8} - \frac{19079}{2}e^{6} + \frac{75332}{15}e^{4} - \frac{2263}{5}e^{2} + \frac{66}{5}$ |
| 89 | $[89, 89, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w + 3]$ | $\phantom{-}\frac{9}{20}e^{18} - \frac{273}{20}e^{16} + \frac{1711}{10}e^{14} - \frac{5724}{5}e^{12} + \frac{22003}{5}e^{10} - \frac{193869}{20}e^{8} + \frac{226627}{20}e^{6} - 5485e^{4} + \frac{551}{5}e^{2} + \frac{66}{5}$ |
| 89 | $[89, 89, w^{5} + w^{4} - 6w^{3} - 6w^{2} + 6w + 3]$ | $\phantom{-}\frac{1}{5}e^{19} - \frac{31}{5}e^{17} + \frac{801}{10}e^{15} - \frac{5597}{10}e^{13} + 2296e^{11} - \frac{28049}{5}e^{9} + \frac{39391}{5}e^{7} - \frac{57277}{10}e^{5} + \frac{16723}{10}e^{3} - \frac{547}{5}e$ |
| 89 | $[89, 89, 2w^{4} - w^{3} - 9w^{2} + w + 5]$ | $\phantom{-}\frac{8}{15}e^{18} - \frac{49}{3}e^{16} + \frac{3109}{15}e^{14} - \frac{21139}{15}e^{12} + \frac{83036}{15}e^{10} - \frac{188606}{15}e^{8} + \frac{77179}{5}e^{6} - \frac{125041}{15}e^{4} + \frac{11611}{15}e^{2} - 16$ |
| 101 | $[101, 101, w^{5} - 5w^{3} - w^{2} + 5w - 1]$ | $\phantom{-}\frac{1}{5}e^{18} - \frac{181}{30}e^{16} + \frac{751}{10}e^{14} - \frac{7468}{15}e^{12} + 1889e^{10} - \frac{61127}{15}e^{8} + \frac{45667}{10}e^{6} - \frac{19137}{10}e^{4} - \frac{3293}{15}e^{2} + \frac{103}{5}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 5w + 1]$ | $1$ |