Base field \(\Q(\sqrt{110}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 110\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 44x^{6} + 498x^{4} + 532x^{2} + 49\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-\frac{31}{2408}e^{7} - \frac{1371}{2408}e^{5} - \frac{15767}{2408}e^{3} - \frac{2737}{344}e$ |
| 5 | $[5, 5, w]$ | $-\frac{31}{2408}e^{7} - \frac{1371}{2408}e^{5} - \frac{15767}{2408}e^{3} - \frac{3081}{344}e$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{1}{86}e^{6} + \frac{47}{86}e^{4} + \frac{553}{86}e^{2} + \frac{41}{86}$ |
| 11 | $[11, 11, -w + 11]$ | $-\frac{1}{86}e^{6} - \frac{47}{86}e^{4} - \frac{553}{86}e^{2} - \frac{127}{86}$ |
| 17 | $[17, 17, w + 5]$ | $-\frac{5}{1204}e^{7} - \frac{48}{301}e^{5} - \frac{1475}{1204}e^{3} + \frac{357}{86}e$ |
| 17 | $[17, 17, w + 12]$ | $-\frac{5}{1204}e^{7} - \frac{48}{301}e^{5} - \frac{1475}{1204}e^{3} + \frac{357}{86}e$ |
| 23 | $[23, 23, w + 8]$ | $-\frac{55}{2408}e^{7} - \frac{2413}{2408}e^{5} - \frac{26459}{2408}e^{3} - \frac{1563}{344}e$ |
| 23 | $[23, 23, w + 15]$ | $-\frac{55}{2408}e^{7} - \frac{2413}{2408}e^{5} - \frac{26459}{2408}e^{3} - \frac{1563}{344}e$ |
| 29 | $[29, 29, w + 9]$ | $\phantom{-}\frac{5}{602}e^{6} + \frac{96}{301}e^{4} + \frac{1475}{602}e^{2} - \frac{185}{43}$ |
| 29 | $[29, 29, -w + 9]$ | $\phantom{-}\frac{5}{602}e^{6} + \frac{96}{301}e^{4} + \frac{1475}{602}e^{2} - \frac{185}{43}$ |
| 37 | $[37, 37, w + 6]$ | $\phantom{-}\frac{29}{344}e^{7} + \frac{1277}{344}e^{5} + \frac{14317}{344}e^{3} + \frac{12369}{344}e$ |
| 37 | $[37, 37, w + 31]$ | $\phantom{-}\frac{29}{344}e^{7} + \frac{1277}{344}e^{5} + \frac{14317}{344}e^{3} + \frac{12369}{344}e$ |
| 43 | $[43, 43, w + 14]$ | $\phantom{-}\frac{31}{602}e^{7} + \frac{1371}{602}e^{5} + \frac{15767}{602}e^{3} + \frac{2737}{86}e$ |
| 43 | $[43, 43, w + 29]$ | $\phantom{-}\frac{31}{602}e^{7} + \frac{1371}{602}e^{5} + \frac{15767}{602}e^{3} + \frac{2737}{86}e$ |
| 47 | $[47, 47, w + 4]$ | $\phantom{-}0$ |
| 47 | $[47, 47, w + 43]$ | $\phantom{-}0$ |
| 49 | $[49, 7, -7]$ | $-\frac{1}{86}e^{6} - \frac{47}{86}e^{4} - \frac{553}{86}e^{2} - \frac{815}{86}$ |
| 53 | $[53, 53, w + 2]$ | $-\frac{1}{14}e^{7} - \frac{22}{7}e^{5} - \frac{491}{14}e^{3} - 27e$ |
| 53 | $[53, 53, w + 51]$ | $-\frac{1}{14}e^{7} - \frac{22}{7}e^{5} - \frac{491}{14}e^{3} - 27e$ |
| 59 | $[59, 59, -w - 13]$ | $-\frac{3}{172}e^{6} - \frac{141}{172}e^{4} - \frac{1659}{172}e^{2} - \frac{1069}{172}$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).