Base field 5.5.38569.1
Generator \(w\), with minimal polynomial \(x^5 - 5 x^3 + 4 x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[67, 67, -w^3 + w^2 + 3 w - 4]$ |
| 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:
| \(x^6 - 6 x^5 - 14 x^4 + 128 x^3 - 122 x^2 - 334 x + 486\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, -w^2 + 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w^3 + w^2 + 4 w - 2]$ | $-\frac{49}{11} e^5 + \frac{175}{11} e^4 + 101 e^3 - \frac{3577}{11} e^2 - \frac{2698}{11} e + \frac{9820}{11}$ |
| 11 | $[11, 11, w^3 - 3 w]$ | $-\frac{69}{11} e^5 + \frac{248}{11} e^4 + 142 e^3 - \frac{5070}{11} e^2 - \frac{3777}{11} e + \frac{13944}{11}$ |
| 13 | $[13, 13, w^4 - 5 w^2 + 2]$ | $\phantom{-}\frac{69}{11} e^5 - \frac{248}{11} e^4 - 142 e^3 + \frac{5070}{11} e^2 + \frac{3777}{11} e - \frac{13900}{11}$ |
| 17 | $[17, 17, w^3 - 3 w - 1]$ | $-\frac{9}{11} e^5 + \frac{29}{11} e^4 + 19 e^3 - \frac{580}{11} e^2 - \frac{562}{11} e + \frac{1594}{11}$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}\frac{108}{11} e^5 - \frac{392}{11} e^4 - 222 e^3 + \frac{8038}{11} e^2 + \frac{5897}{11} e - \frac{22197}{11}$ |
| 37 | $[37, 37, w^4 + w^3 - 5 w^2 - 5 w + 4]$ | $\phantom{-}\frac{181}{11} e^5 - \frac{648}{11} e^4 - 373 e^3 + \frac{13246}{11} e^2 + \frac{9969}{11} e - \frac{36352}{11}$ |
| 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 | $[43, 43, -w^4 + w^3 + 4 w^2 - 2 w - 2]$ | $-\frac{157}{11} e^5 + \frac{567}{11} e^4 + 323 e^3 - \frac{11615}{11} e^2 - \frac{8595}{11} e + \frac{32006}{11}$ |
| 47 | $[47, 47, -w^4 - w^3 + 6 w^2 + 4 w - 5]$ | $-7 e^5 + 25 e^4 + 159 e^3 - 511 e^2 - 390 e + 1404$ |
| 59 | $[59, 59, w^4 + w^3 - 6 w^2 - 4 w + 4]$ | $\phantom{-}\frac{152}{11} e^5 - \frac{546}{11} e^4 - 313 e^3 + \frac{11173}{11} e^2 + \frac{8350}{11} e - \frac{30766}{11}$ |
| 67 | $[67, 67, -w^3 + w^2 + 3 w - 4]$ | $\phantom{-}1$ |
| 73 | $[73, 73, w^4 - 3 w^2 - w - 1]$ | $\phantom{-}\frac{141}{11} e^5 - \frac{502}{11} e^4 - 291 e^3 + \frac{10238}{11} e^2 + \frac{7844}{11} e - \frac{28016}{11}$ |
| 73 | $[73, 73, -2 w^4 - w^3 + 9 w^2 + 5 w - 6]$ | $-\frac{335}{11} e^5 + \frac{1209}{11} e^4 + 689 e^3 - \frac{24763}{11} e^2 - \frac{18285}{11} e + \frac{68230}{11}$ |
| 79 | $[79, 79, -3 w^4 + 13 w^2 + 2 w - 7]$ | $\phantom{-}\frac{104}{11} e^5 - \frac{373}{11} e^4 - 214 e^3 + \frac{7614}{11} e^2 + \frac{5690}{11} e - \frac{20842}{11}$ |
| 79 | $[79, 79, -w^3 + 5 w]$ | $-\frac{1}{11} e^5 + \frac{13}{11} e^4 + e^3 - \frac{315}{11} e^2 + \frac{50}{11} e + \frac{1040}{11}$ |
| 79 | $[79, 79, -w^4 + 3 w^2 + 1]$ | $\phantom{-}\frac{189}{11} e^5 - \frac{686}{11} e^4 - 388 e^3 + \frac{14061}{11} e^2 + \frac{10207}{11} e - \frac{38710}{11}$ |
| 83 | $[83, 83, -2 w^4 - 2 w^3 + 11 w^2 + 7 w - 8]$ | $\phantom{-}\frac{161}{11} e^5 - \frac{575}{11} e^4 - 332 e^3 + \frac{11742}{11} e^2 + \frac{8890}{11} e - \frac{32228}{11}$ |
| 89 | $[89, 89, -w^4 - 2 w^3 + 4 w^2 + 7 w - 3]$ | $\phantom{-}\frac{10}{11} e^5 - \frac{42}{11} e^4 - 20 e^3 + \frac{906}{11} e^2 + \frac{479}{11} e - \frac{2700}{11}$ |
| 101 | $[101, 101, -w^4 + 5 w^2 - w - 4]$ | $-\frac{124}{11} e^5 + \frac{457}{11} e^4 + 254 e^3 - \frac{9404}{11} e^2 - \frac{6670}{11} e + \frac{26088}{11}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $67$ | $[67, 67, -w^3 + w^2 + 3 w - 4]$ | $-1$ |