Base field \(\Q(\sqrt{70}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 70\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8, 4, 2w]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 19x^{10} + 132x^{8} - 411x^{6} + 565x^{4} - 264x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{9}{62}e^{11} - \frac{161}{62}e^{9} + \frac{508}{31}e^{7} - \frac{2701}{62}e^{5} + \frac{93}{2}e^{3} - \frac{444}{31}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -3w + 25]$ | $\phantom{-}\frac{11}{124}e^{11} - \frac{183}{124}e^{9} + \frac{521}{62}e^{7} - \frac{2385}{124}e^{5} + \frac{71}{4}e^{3} - \frac{491}{62}e$ |
| 7 | $[7, 7, w]$ | $\phantom{-}\frac{6}{31}e^{10} - \frac{97}{31}e^{8} + \frac{512}{31}e^{6} - \frac{943}{31}e^{4} + 12e^{2} + \frac{90}{31}$ |
| 11 | $[11, 11, w - 9]$ | $\phantom{-}\frac{5}{62}e^{10} - \frac{43}{31}e^{8} + \frac{265}{31}e^{6} - \frac{1411}{62}e^{4} + 24e^{2} - \frac{102}{31}$ |
| 11 | $[11, 11, -w - 9]$ | $-\frac{17}{62}e^{10} + \frac{140}{31}e^{8} - \frac{777}{31}e^{6} + \frac{3297}{62}e^{4} - 36e^{2} + \frac{74}{31}$ |
| 17 | $[17, 17, w + 6]$ | $-\frac{9}{62}e^{11} + \frac{65}{31}e^{9} - \frac{260}{31}e^{7} + \frac{97}{62}e^{5} + 32e^{3} - \frac{734}{31}e$ |
| 17 | $[17, 17, w + 11]$ | $-\frac{11}{62}e^{11} + \frac{107}{31}e^{9} - \frac{769}{31}e^{7} + \frac{4989}{62}e^{5} - 114e^{3} + \frac{1638}{31}e$ |
| 23 | $[23, 23, w + 1]$ | $-\frac{13}{62}e^{10} + \frac{205}{62}e^{8} - \frac{534}{31}e^{6} + \frac{2069}{62}e^{4} - \frac{45}{2}e^{2} + \frac{135}{31}$ |
| 23 | $[23, 23, w + 22]$ | $\phantom{-}\frac{21}{62}e^{10} - \frac{355}{62}e^{8} + \frac{1020}{31}e^{6} - \frac{4587}{62}e^{4} + \frac{117}{2}e^{2} - \frac{323}{31}$ |
| 31 | $[31, 31, 4w - 33]$ | $-\frac{2}{31}e^{11} + \frac{22}{31}e^{9} + \frac{5}{31}e^{7} - \frac{688}{31}e^{5} + 65e^{3} - \frac{1394}{31}e$ |
| 31 | $[31, 31, 4w + 33]$ | $-\frac{3}{31}e^{11} + \frac{64}{31}e^{9} - \frac{504}{31}e^{7} + \frac{1758}{31}e^{5} - 81e^{3} + \frac{978}{31}e$ |
| 37 | $[37, 37, w + 12]$ | $\phantom{-}\frac{1}{31}e^{10} - \frac{11}{31}e^{8} + \frac{13}{31}e^{6} + \frac{189}{31}e^{4} - 18e^{2} + \frac{108}{31}$ |
| 37 | $[37, 37, w + 25]$ | $-\frac{5}{31}e^{10} + \frac{86}{31}e^{8} - \frac{499}{31}e^{6} + \frac{1070}{31}e^{4} - 18e^{2} - \frac{168}{31}$ |
| 53 | $[53, 53, w + 21]$ | $\phantom{-}\frac{18}{31}e^{10} - \frac{291}{31}e^{8} + \frac{1536}{31}e^{6} - \frac{2829}{31}e^{4} + 38e^{2} + \frac{84}{31}$ |
| 53 | $[53, 53, w + 32]$ | $\phantom{-}\frac{6}{31}e^{10} - \frac{97}{31}e^{8} + \frac{512}{31}e^{6} - \frac{943}{31}e^{4} + 10e^{2} + \frac{276}{31}$ |
| 61 | $[61, 61, -w - 3]$ | $-\frac{47}{124}e^{11} + \frac{827}{124}e^{9} - \frac{2553}{62}e^{7} + \frac{13313}{124}e^{5} - \frac{479}{4}e^{3} + \frac{3259}{62}e$ |
| 61 | $[61, 61, w - 3]$ | $-\frac{27}{124}e^{11} + \frac{483}{124}e^{9} - \frac{1555}{62}e^{7} + \frac{8785}{124}e^{5} - \frac{343}{4}e^{3} + \frac{1859}{62}e$ |
| 73 | $[73, 73, w + 17]$ | $\phantom{-}\frac{9}{31}e^{11} - \frac{130}{31}e^{9} + \frac{520}{31}e^{7} - \frac{66}{31}e^{5} - 73e^{3} + \frac{2026}{31}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |