Base field 5.5.38569.1
Generator \(w\), with minimal polynomial \(x^{5} - 5x^{3} + 4x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[67, 67, -w^{3} + w^{2} + 3w - 4]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 6x^{5} - 14x^{4} + 128x^{3} - 122x^{2} - 334x + 486\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w^{3} + w^{2} + 4w - 2]$ | $-\frac{49}{11}e^{5} + \frac{175}{11}e^{4} + 101e^{3} - \frac{3577}{11}e^{2} - \frac{2698}{11}e + \frac{9820}{11}$ |
| 11 | $[11, 11, w^{3} - 3w]$ | $-\frac{69}{11}e^{5} + \frac{248}{11}e^{4} + 142e^{3} - \frac{5070}{11}e^{2} - \frac{3777}{11}e + \frac{13944}{11}$ |
| 13 | $[13, 13, w^{4} - 5w^{2} + 2]$ | $\phantom{-}\frac{69}{11}e^{5} - \frac{248}{11}e^{4} - 142e^{3} + \frac{5070}{11}e^{2} + \frac{3777}{11}e - \frac{13900}{11}$ |
| 17 | $[17, 17, w^{3} - 3w - 1]$ | $-\frac{9}{11}e^{5} + \frac{29}{11}e^{4} + 19e^{3} - \frac{580}{11}e^{2} - \frac{562}{11}e + \frac{1594}{11}$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}\frac{108}{11}e^{5} - \frac{392}{11}e^{4} - 222e^{3} + \frac{8038}{11}e^{2} + \frac{5897}{11}e - \frac{22197}{11}$ |
| 37 | $[37, 37, w^{4} + w^{3} - 5w^{2} - 5w + 4]$ | $\phantom{-}\frac{181}{11}e^{5} - \frac{648}{11}e^{4} - 373e^{3} + \frac{13246}{11}e^{2} + \frac{9969}{11}e - \frac{36352}{11}$ |
| 43 | $[43, 43, w^{2} + w - 3]$ | $-\frac{1}{11}e^{5} + \frac{13}{11}e^{4} + e^{3} - \frac{315}{11}e^{2} + \frac{94}{11}e + \frac{1018}{11}$ |
| 43 | $[43, 43, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $-\frac{157}{11}e^{5} + \frac{567}{11}e^{4} + 323e^{3} - \frac{11615}{11}e^{2} - \frac{8595}{11}e + \frac{32006}{11}$ |
| 47 | $[47, 47, -w^{4} - w^{3} + 6w^{2} + 4w - 5]$ | $-7e^{5} + 25e^{4} + 159e^{3} - 511e^{2} - 390e + 1404$ |
| 59 | $[59, 59, w^{4} + w^{3} - 6w^{2} - 4w + 4]$ | $\phantom{-}\frac{152}{11}e^{5} - \frac{546}{11}e^{4} - 313e^{3} + \frac{11173}{11}e^{2} + \frac{8350}{11}e - \frac{30766}{11}$ |
| 67 | $[67, 67, -w^{3} + w^{2} + 3w - 4]$ | $\phantom{-}1$ |
| 73 | $[73, 73, w^{4} - 3w^{2} - w - 1]$ | $\phantom{-}\frac{141}{11}e^{5} - \frac{502}{11}e^{4} - 291e^{3} + \frac{10238}{11}e^{2} + \frac{7844}{11}e - \frac{28016}{11}$ |
| 73 | $[73, 73, -2w^{4} - w^{3} + 9w^{2} + 5w - 6]$ | $-\frac{335}{11}e^{5} + \frac{1209}{11}e^{4} + 689e^{3} - \frac{24763}{11}e^{2} - \frac{18285}{11}e + \frac{68230}{11}$ |
| 79 | $[79, 79, -3w^{4} + 13w^{2} + 2w - 7]$ | $\phantom{-}\frac{104}{11}e^{5} - \frac{373}{11}e^{4} - 214e^{3} + \frac{7614}{11}e^{2} + \frac{5690}{11}e - \frac{20842}{11}$ |
| 79 | $[79, 79, -w^{3} + 5w]$ | $-\frac{1}{11}e^{5} + \frac{13}{11}e^{4} + e^{3} - \frac{315}{11}e^{2} + \frac{50}{11}e + \frac{1040}{11}$ |
| 79 | $[79, 79, -w^{4} + 3w^{2} + 1]$ | $\phantom{-}\frac{189}{11}e^{5} - \frac{686}{11}e^{4} - 388e^{3} + \frac{14061}{11}e^{2} + \frac{10207}{11}e - \frac{38710}{11}$ |
| 83 | $[83, 83, -2w^{4} - 2w^{3} + 11w^{2} + 7w - 8]$ | $\phantom{-}\frac{161}{11}e^{5} - \frac{575}{11}e^{4} - 332e^{3} + \frac{11742}{11}e^{2} + \frac{8890}{11}e - \frac{32228}{11}$ |
| 89 | $[89, 89, -w^{4} - 2w^{3} + 4w^{2} + 7w - 3]$ | $\phantom{-}\frac{10}{11}e^{5} - \frac{42}{11}e^{4} - 20e^{3} + \frac{906}{11}e^{2} + \frac{479}{11}e - \frac{2700}{11}$ |
| 101 | $[101, 101, -w^{4} + 5w^{2} - w - 4]$ | $-\frac{124}{11}e^{5} + \frac{457}{11}e^{4} + 254e^{3} - \frac{9404}{11}e^{2} - \frac{6670}{11}e + \frac{26088}{11}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $67$ | $[67, 67, -w^{3} + w^{2} + 3w - 4]$ | $-1$ |