Base field 4.4.13068.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 4, 3w^{3} - 5w^{2} - 15w + 6]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 112x^{6} + 3824x^{4} - 41600x^{2} + 40000\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{3} - w^{2} - 6w - 2]$ | $-\frac{1}{112000}e^{7} - \frac{11}{14000}e^{5} + \frac{1697}{14000}e^{3} - \frac{167}{70}e$ |
| 3 | $[3, 3, -w^{3} + 2w^{2} + 4w - 2]$ | $\phantom{-}\frac{1}{2800}e^{6} - \frac{87}{2800}e^{4} + \frac{114}{175}e^{2} - \frac{15}{14}$ |
| 4 | $[4, 2, w^{3} - w^{2} - 5w - 2]$ | $\phantom{-}0$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ | $-\frac{1}{56000}e^{7} - \frac{11}{7000}e^{5} + \frac{1697}{7000}e^{3} - \frac{202}{35}e$ |
| 17 | $[17, 17, -w + 2]$ | $\phantom{-}e$ |
| 29 | $[29, 29, -w^{3} + 2w^{2} + 4w - 4]$ | $-\frac{41}{112000}e^{7} + \frac{1023}{28000}e^{5} - \frac{13723}{14000}e^{3} + \frac{957}{140}e$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 4w]$ | $\phantom{-}\frac{1}{16000}e^{7} - \frac{7}{1000}e^{5} + \frac{603}{2000}e^{3} - \frac{28}{5}e$ |
| 31 | $[31, 31, -w^{2} + 2]$ | $-\frac{1}{11200}e^{6} - \frac{11}{1400}e^{4} + \frac{997}{1400}e^{2} - \frac{34}{7}$ |
| 31 | $[31, 31, -w^{3} + 7w + 5]$ | $-\frac{1}{1600}e^{6} + \frac{7}{100}e^{4} - \frac{403}{200}e^{2} + 9$ |
| 41 | $[41, 41, -2w^{3} + 2w^{2} + 13w - 2]$ | $\phantom{-}\frac{27}{112000}e^{7} - \frac{403}{14000}e^{5} + \frac{15081}{14000}e^{3} - \frac{179}{14}e$ |
| 41 | $[41, 41, 3w^{3} - 4w^{2} - 17w + 5]$ | $-\frac{3}{16000}e^{7} + \frac{59}{4000}e^{5} - \frac{409}{2000}e^{3} - \frac{7}{20}e$ |
| 67 | $[67, 67, 3w^{3} - 4w^{2} - 17w + 1]$ | $\phantom{-}\frac{3}{1400}e^{6} - \frac{261}{1400}e^{4} + \frac{1193}{350}e^{2} + \frac{32}{7}$ |
| 67 | $[67, 67, -w^{2} + 4w + 2]$ | $-\frac{1}{1400}e^{6} + \frac{87}{1400}e^{4} - \frac{281}{350}e^{2} - \frac{48}{7}$ |
| 83 | $[83, 83, 2w^{2} - 5w - 2]$ | $-\frac{1}{4480}e^{7} + \frac{17}{560}e^{5} - \frac{739}{560}e^{3} + \frac{1299}{70}e$ |
| 83 | $[83, 83, -w^{3} + 8w + 6]$ | $-\frac{79}{112000}e^{7} + \frac{1937}{28000}e^{5} - \frac{26237}{14000}e^{3} + \frac{383}{28}e$ |
| 83 | $[83, 83, w^{3} - 2w^{2} - 2w - 2]$ | $\phantom{-}\frac{3}{16000}e^{7} - \frac{59}{4000}e^{5} + \frac{409}{2000}e^{3} - \frac{13}{20}e$ |
| 83 | $[83, 83, w^{3} - 2w^{2} - 6w]$ | $\phantom{-}\frac{69}{112000}e^{7} - \frac{51}{875}e^{5} + \frac{20807}{14000}e^{3} - \frac{353}{35}e$ |
| 97 | $[97, 97, -3w^{3} + 2w^{2} + 17w + 7]$ | $\phantom{-}\frac{33}{11200}e^{6} - \frac{337}{1400}e^{4} + \frac{5599}{1400}e^{2} + \frac{44}{7}$ |
| 97 | $[97, 97, w^{3} - 4w^{2} + 3w + 1]$ | $\phantom{-}\frac{1}{1600}e^{6} - \frac{7}{100}e^{4} + \frac{503}{200}e^{2} - 19$ |
| 97 | $[97, 97, -5w^{3} + 8w^{2} + 24w - 8]$ | $-\frac{3}{1400}e^{6} + \frac{261}{1400}e^{4} - \frac{684}{175}e^{2} + \frac{136}{7}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, w^{3} - w^{2} - 5w - 2]$ | $1$ |