Base field 3.3.985.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[17, 17, -w^{2} + 2w + 1]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} - 2x^{8} - 20x^{7} + 48x^{6} + 66x^{5} - 184x^{4} - 28x^{3} + 176x^{2} - 83x + 10\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}\frac{3}{8}e^{8} - \frac{1}{2}e^{7} - \frac{63}{8}e^{6} + \frac{51}{4}e^{5} + \frac{273}{8}e^{4} - \frac{93}{2}e^{3} - \frac{365}{8}e^{2} + \frac{145}{4}e - 1$ |
| 7 | $[7, 7, -w + 2]$ | $-\frac{1}{4}e^{8} + \frac{1}{2}e^{7} + 5e^{6} - \frac{47}{4}e^{5} - \frac{67}{4}e^{4} + \frac{83}{2}e^{3} + \frac{27}{2}e^{2} - \frac{137}{4}e + \frac{19}{2}$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{2}e^{8} - \frac{3}{4}e^{7} - \frac{21}{2}e^{6} + 19e^{5} + \frac{89}{2}e^{4} - \frac{301}{4}e^{3} - \frac{103}{2}e^{2} + 72e - 15$ |
| 11 | $[11, 11, -w^{2} + 2w + 2]$ | $-\frac{5}{8}e^{8} + e^{7} + \frac{103}{8}e^{6} - \frac{99}{4}e^{5} - \frac{407}{8}e^{4} + \frac{185}{2}e^{3} + \frac{453}{8}e^{2} - \frac{327}{4}e + 16$ |
| 17 | $[17, 17, -w - 3]$ | $\phantom{-}\frac{3}{4}e^{8} - \frac{9}{8}e^{7} - \frac{31}{2}e^{6} + \frac{227}{8}e^{5} + \frac{125}{2}e^{4} - \frac{867}{8}e^{3} - 70e^{2} + \frac{809}{8}e - \frac{67}{4}$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{2} + w + 4]$ | $\phantom{-}\frac{1}{2}e^{8} - e^{7} - 10e^{6} + \frac{95}{4}e^{5} + \frac{67}{2}e^{4} - \frac{175}{2}e^{3} - \frac{49}{2}e^{2} + \frac{327}{4}e - \frac{41}{2}$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}\frac{3}{8}e^{8} - \frac{1}{2}e^{7} - \frac{65}{8}e^{6} + 13e^{5} + \frac{309}{8}e^{4} - \frac{107}{2}e^{3} - \frac{451}{8}e^{2} + 54e - \frac{1}{2}$ |
| 27 | $[27, 3, -3]$ | $-\frac{1}{8}e^{8} + \frac{1}{2}e^{7} + \frac{19}{8}e^{6} - 11e^{5} - \frac{31}{8}e^{4} + 43e^{3} - \frac{71}{8}e^{2} - \frac{91}{2}e + \frac{37}{2}$ |
| 29 | $[29, 29, w^{2} - w - 8]$ | $-\frac{3}{4}e^{8} + \frac{5}{4}e^{7} + 15e^{6} - \frac{61}{2}e^{5} - \frac{209}{4}e^{4} + \frac{433}{4}e^{3} + 43e^{2} - 94e + 24$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $-\frac{5}{8}e^{8} + \frac{3}{4}e^{7} + \frac{107}{8}e^{6} - \frac{79}{4}e^{5} - \frac{495}{8}e^{4} + \frac{305}{4}e^{3} + \frac{689}{8}e^{2} - \frac{265}{4}e + 5$ |
| 29 | $[29, 29, w^{2} - w - 1]$ | $\phantom{-}\frac{11}{8}e^{8} - 2e^{7} - \frac{229}{8}e^{6} + \frac{203}{4}e^{5} + \frac{949}{8}e^{4} - 195e^{3} - \frac{1091}{8}e^{2} + \frac{717}{4}e - 32$ |
| 31 | $[31, 31, w^{2} - 2]$ | $-\frac{5}{4}e^{8} + \frac{15}{8}e^{7} + \frac{103}{4}e^{6} - \frac{375}{8}e^{5} - \frac{205}{2}e^{4} + \frac{1381}{8}e^{3} + \frac{453}{4}e^{2} - \frac{1197}{8}e + \frac{123}{4}$ |
| 37 | $[37, 37, 2w - 5]$ | $\phantom{-}\frac{3}{8}e^{8} - \frac{3}{4}e^{7} - \frac{61}{8}e^{6} + \frac{73}{4}e^{5} + \frac{217}{8}e^{4} - \frac{297}{4}e^{3} - \frac{135}{8}e^{2} + \frac{303}{4}e - 23$ |
| 43 | $[43, 43, w^{2} - 2w - 5]$ | $-\frac{1}{4}e^{8} + \frac{1}{4}e^{7} + \frac{11}{2}e^{6} - \frac{27}{4}e^{5} - \frac{113}{4}e^{4} + \frac{99}{4}e^{3} + \frac{101}{2}e^{2} - \frac{69}{4}e - \frac{21}{2}$ |
| 47 | $[47, 47, w^{2} - 3w - 2]$ | $\phantom{-}\frac{1}{2}e^{8} - e^{7} - \frac{41}{4}e^{6} + \frac{95}{4}e^{5} + 38e^{4} - \frac{179}{2}e^{3} - \frac{151}{4}e^{2} + \frac{319}{4}e - \frac{27}{2}$ |
| 49 | $[49, 7, w^{2} + w - 4]$ | $\phantom{-}\frac{3}{8}e^{8} - \frac{3}{4}e^{7} - \frac{59}{8}e^{6} + \frac{35}{2}e^{5} + \frac{181}{8}e^{4} - \frac{239}{4}e^{3} - \frac{97}{8}e^{2} + 51e - \frac{31}{2}$ |
| 53 | $[53, 53, w^{2} - 2w - 6]$ | $-\frac{3}{2}e^{8} + \frac{15}{8}e^{7} + \frac{127}{4}e^{6} - \frac{395}{8}e^{5} - \frac{567}{4}e^{4} + \frac{1549}{8}e^{3} + \frac{739}{4}e^{2} - \frac{1417}{8}e + \frac{79}{4}$ |
| 71 | $[71, 71, w - 5]$ | $\phantom{-}\frac{7}{8}e^{8} - \frac{5}{4}e^{7} - \frac{143}{8}e^{6} + 31e^{5} + \frac{561}{8}e^{4} - \frac{415}{4}e^{3} - \frac{693}{8}e^{2} + 72e - \frac{3}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{2} + 2w + 1]$ | $-1$ |