Base field \(\Q(\sqrt{85}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 21\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[17, 17, w + 8]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $42$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 4x^{7} - 10x^{6} - 56x^{5} - 11x^{4} + 177x^{3} + 172x^{2} - 7x - 7\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-\frac{4}{263}e^{7} - \frac{87}{263}e^{6} + \frac{8}{263}e^{5} + \frac{1155}{263}e^{4} + \frac{623}{263}e^{3} - \frac{3523}{263}e^{2} - \frac{2797}{263}e + \frac{154}{263}$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}\frac{63}{263}e^{7} + \frac{121}{263}e^{6} - \frac{915}{263}e^{5} - \frac{1688}{263}e^{4} + \frac{3272}{263}e^{3} + \frac{5320}{263}e^{2} - \frac{1512}{263}e - \frac{453}{263}$ |
| 5 | $[5, 5, w + 2]$ | $-\frac{6}{263}e^{7} + \frac{1}{263}e^{6} + \frac{12}{263}e^{5} + \frac{23}{263}e^{4} + \frac{540}{263}e^{3} - \frac{156}{263}e^{2} - \frac{1960}{263}e - \frac{295}{263}$ |
| 7 | $[7, 7, w]$ | $\phantom{-}\frac{132}{263}e^{7} + \frac{241}{263}e^{6} - \frac{1842}{263}e^{5} - \frac{3399}{263}e^{4} + \frac{6004}{263}e^{3} + \frac{10533}{263}e^{2} - \frac{1064}{263}e - \frac{348}{263}$ |
| 7 | $[7, 7, w + 6]$ | $-\frac{69}{263}e^{7} - \frac{120}{263}e^{6} + \frac{927}{263}e^{5} + \frac{1711}{263}e^{4} - \frac{2732}{263}e^{3} - \frac{5213}{263}e^{2} - \frac{448}{263}e - \frac{894}{263}$ |
| 17 | $[17, 17, w + 8]$ | $\phantom{-}1$ |
| 19 | $[19, 19, w + 1]$ | $-\frac{58}{263}e^{7} - \frac{78}{263}e^{6} + \frac{905}{263}e^{5} + \frac{1099}{263}e^{4} - \frac{3722}{263}e^{3} - \frac{3612}{263}e^{2} + \frac{2970}{263}e + \frac{1181}{263}$ |
| 19 | $[19, 19, w - 2]$ | $-\frac{121}{263}e^{7} - \frac{199}{263}e^{6} + \frac{1820}{263}e^{5} + \frac{2787}{263}e^{4} - \frac{7257}{263}e^{3} - \frac{8669}{263}e^{2} + \frac{6060}{263}e + \frac{845}{263}$ |
| 23 | $[23, 23, w + 9]$ | $-\frac{19}{263}e^{7} + \frac{47}{263}e^{6} + \frac{301}{263}e^{5} - \frac{497}{263}e^{4} - \frac{1709}{263}e^{3} + \frac{821}{263}e^{2} + \frac{3612}{263}e + \frac{863}{263}$ |
| 23 | $[23, 23, w + 13]$ | $-\frac{115}{263}e^{7} - \frac{200}{263}e^{6} + \frac{1545}{263}e^{5} + \frac{2764}{263}e^{4} - \frac{4378}{263}e^{3} - \frac{8250}{263}e^{2} - \frac{1974}{263}e - \frac{964}{263}$ |
| 37 | $[37, 37, w + 11]$ | $\phantom{-}\frac{314}{263}e^{7} + \frac{649}{263}e^{6} - \frac{4047}{263}e^{5} - \frac{9269}{263}e^{4} + \frac{9875}{263}e^{3} + \frac{29467}{263}e^{2} + \frac{10611}{263}e - \frac{1569}{263}$ |
| 37 | $[37, 37, w + 25]$ | $-\frac{217}{263}e^{7} - \frac{446}{263}e^{6} + \frac{3064}{263}e^{5} + \frac{6311}{263}e^{4} - \frac{9926}{263}e^{3} - \frac{19844}{263}e^{2} + \frac{211}{263}e - \frac{456}{263}$ |
| 59 | $[59, 59, 3w + 10]$ | $-\frac{162}{263}e^{7} - \frac{499}{263}e^{6} + \frac{1902}{263}e^{5} + \frac{6933}{263}e^{4} - \frac{2252}{263}e^{3} - \frac{21833}{263}e^{2} - \frac{15048}{263}e + \frac{1240}{263}$ |
| 59 | $[59, 59, 3w - 13]$ | $-\frac{71}{263}e^{7} - \frac{32}{263}e^{6} + \frac{931}{263}e^{5} + \frac{579}{263}e^{4} - \frac{3078}{263}e^{3} - \frac{2109}{263}e^{2} + \frac{2756}{263}e + \frac{498}{263}$ |
| 73 | $[73, 73, w + 15]$ | $\phantom{-}\frac{214}{263}e^{7} + \frac{315}{263}e^{6} - \frac{3058}{263}e^{5} - \frac{4590}{263}e^{4} + \frac{10985}{263}e^{3} + \frac{15032}{263}e^{2} - \frac{6451}{263}e - \frac{2453}{263}$ |
| 73 | $[73, 73, w + 57]$ | $\phantom{-}\frac{113}{263}e^{7} + \frac{288}{263}e^{6} - \frac{1541}{263}e^{5} - \frac{3896}{263}e^{4} + \frac{4295}{263}e^{3} + \frac{11880}{263}e^{2} + \frac{2811}{263}e - \frac{1326}{263}$ |
| 89 | $[89, 89, -w - 10]$ | $\phantom{-}\frac{582}{263}e^{7} + \frac{1218}{263}e^{6} - \frac{8002}{263}e^{5} - \frac{17222}{263}e^{4} + \frac{24153}{263}e^{3} + \frac{54056}{263}e^{2} + \frac{5494}{263}e + \frac{474}{263}$ |
| 89 | $[89, 89, w - 11]$ | $-\frac{689}{263}e^{7} - \frac{1507}{263}e^{6} + \frac{9005}{263}e^{5} + \frac{21358}{263}e^{4} - \frac{22939}{263}e^{3} - \frac{67358}{263}e^{2} - \frac{20810}{263}e + \frac{2462}{263}$ |
| 97 | $[97, 97, w + 22]$ | $-\frac{92}{263}e^{7} - \frac{160}{263}e^{6} + \frac{1499}{263}e^{5} + \frac{2106}{263}e^{4} - \frac{6974}{263}e^{3} - \frac{6337}{263}e^{2} + \frac{8783}{263}e + \frac{2227}{263}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, w + 8]$ | $-1$ |