Base field 4.4.14656.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 4 x^2 + 4 x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, w^2 - 3]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^9 + 3 x^8 - 8 x^7 - 27 x^6 + 13 x^5 + 69 x^4 + 13 x^3 - 40 x^2 - 10 x + 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $-\frac{1}{2} e^6 - \frac{1}{2} e^5 + \frac{9}{2} e^4 + \frac{5}{2} e^3 - \frac{21}{2} e^2 - \frac{5}{2} e + \frac{7}{2}$ |
| 5 | $[5, 5, -w^2 + w + 1]$ | $-\frac{1}{2} e^8 - \frac{3}{2} e^7 + \frac{9}{2} e^6 + \frac{27}{2} e^5 - \frac{23}{2} e^4 - \frac{65}{2} e^3 + \frac{13}{2} e^2 + 12 e - 2$ |
| 11 | $[11, 11, w^2 - 3]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^2 + w + 3]$ | $\phantom{-}\frac{3}{2} e^8 + 3 e^7 - 14 e^6 - 25 e^5 + 35 e^4 + 57 e^3 - 15 e^2 - \frac{43}{2} e + 2$ |
| 19 | $[19, 19, -w^3 + 2 w^2 + 3 w - 1]$ | $\phantom{-}2 e^8 + \frac{7}{2} e^7 - \frac{39}{2} e^6 - \frac{57}{2} e^5 + \frac{107}{2} e^4 + \frac{127}{2} e^3 - \frac{71}{2} e^2 - \frac{47}{2} e + 6$ |
| 27 | $[27, 3, w^3 - 3 w^2 - w + 5]$ | $-2 e^8 - 4 e^7 + \frac{41}{2} e^6 + \frac{69}{2} e^5 - \frac{133}{2} e^4 - \frac{167}{2} e^3 + \frac{149}{2} e^2 + \frac{83}{2} e - \frac{47}{2}$ |
| 41 | $[41, 41, -w^3 + 2 w^2 + w - 1]$ | $-\frac{5}{2} e^8 - 5 e^7 + 23 e^6 + 41 e^5 - 56 e^4 - 91 e^3 + 21 e^2 + \frac{65}{2} e - 2$ |
| 41 | $[41, 41, -w^3 + w^2 + 2 w - 1]$ | $\phantom{-}\frac{3}{2} e^8 + 4 e^7 - 14 e^6 - 36 e^5 + 38 e^4 + 89 e^3 - 27 e^2 - \frac{77}{2} e + 9$ |
| 43 | $[43, 43, w^3 - w^2 - 5 w + 1]$ | $\phantom{-}\frac{5}{2} e^8 + \frac{11}{2} e^7 - 24 e^6 - 48 e^5 + 67 e^4 + 118 e^3 - 49 e^2 - \frac{123}{2} e + \frac{13}{2}$ |
| 47 | $[47, 47, w^2 - 2 w - 5]$ | $\phantom{-}\frac{1}{2} e^8 - \frac{1}{2} e^7 - \frac{13}{2} e^6 + \frac{11}{2} e^5 + \frac{45}{2} e^4 - \frac{31}{2} e^3 - \frac{39}{2} e^2 + 12 e$ |
| 47 | $[47, 47, -2 w^3 + 6 w^2 + w - 5]$ | $-e^8 + 12 e^6 - 2 e^5 - 42 e^4 + 7 e^3 + 45 e^2 - e - 14$ |
| 61 | $[61, 61, -2 w^3 + 5 w^2 + 4 w - 7]$ | $\phantom{-}\frac{1}{2} e^8 + 3 e^7 - \frac{7}{2} e^6 - \frac{57}{2} e^5 + \frac{17}{2} e^4 + \frac{149}{2} e^3 - \frac{21}{2} e^2 - 41 e + \frac{9}{2}$ |
| 67 | $[67, 67, -2 w^2 + 2 w + 9]$ | $\phantom{-}\frac{5}{2} e^8 + \frac{13}{2} e^7 - \frac{47}{2} e^6 - \frac{119}{2} e^5 + \frac{125}{2} e^4 + \frac{305}{2} e^3 - \frac{75}{2} e^2 - 80 e + 6$ |
| 67 | $[67, 67, -w^3 + 2 w^2 + 4 w - 1]$ | $-\frac{11}{2} e^8 - 11 e^7 + \frac{107}{2} e^6 + \frac{191}{2} e^5 - \frac{293}{2} e^4 - \frac{465}{2} e^3 + \frac{187}{2} e^2 + 110 e - \frac{37}{2}$ |
| 71 | $[71, 71, w^3 - w^2 - 6 w + 3]$ | $\phantom{-}3 e^8 + 7 e^7 - \frac{57}{2} e^6 - \frac{123}{2} e^5 + \frac{159}{2} e^4 + \frac{301}{2} e^3 - \frac{129}{2} e^2 - \frac{147}{2} e + \frac{41}{2}$ |
| 83 | $[83, 83, -w^3 + 2 w^2 + 5 w + 1]$ | $-\frac{1}{2} e^8 + \frac{13}{2} e^6 - \frac{1}{2} e^5 - \frac{49}{2} e^4 + \frac{3}{2} e^3 + \frac{45}{2} e^2 + \frac{3}{2}$ |
| 89 | $[89, 89, -w - 3]$ | $\phantom{-}\frac{1}{2} e^8 + e^7 - \frac{13}{2} e^6 - \frac{19}{2} e^5 + \frac{61}{2} e^4 + \frac{47}{2} e^3 - \frac{113}{2} e^2 - 12 e + \frac{51}{2}$ |
| 89 | $[89, 89, -w^2 - 2 w + 1]$ | $\phantom{-}2 e^7 + \frac{3}{2} e^6 - \frac{41}{2} e^5 - \frac{17}{2} e^4 + \frac{111}{2} e^3 + \frac{25}{2} e^2 - \frac{61}{2} e - \frac{7}{2}$ |
| 97 | $[97, 97, w^3 - w^2 - 6 w + 1]$ | $\phantom{-}3 e^8 + \frac{9}{2} e^7 - \frac{59}{2} e^6 - \frac{69}{2} e^5 + \frac{163}{2} e^4 + \frac{141}{2} e^3 - \frac{111}{2} e^2 - \frac{35}{2} e + 11$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w^2 - 3]$ | $-1$ |