Base field 4.4.9248.1
Generator \(w\), with minimal polynomial \(x^4 - 5 x^2 + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[26,26,w^3 - 4 w - 3]$ |
| Dimension: | $8$ |
| 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:
| \(x^8 - 3 x^7 - 67 x^6 + 255 x^5 + 1318 x^4 - 6568 x^3 - 4288 x^2 + 52336 x - 60832\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{1}{64} e^7 + \frac{1}{64} e^6 - \frac{63}{64} e^5 + \frac{7}{64} e^4 + \frac{673}{32} e^3 - \frac{343}{16} e^2 - \frac{1195}{8} e + 254$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -w^2 + w + 3]$ | $\phantom{-}1$ |
| 13 | $[13, 13, w^2 + w - 3]$ | $\phantom{-}e$ |
| 19 | $[19, 19, -w^3 + 3 w + 1]$ | $\phantom{-}\frac{11}{64} e^7 + \frac{13}{64} e^6 - \frac{679}{64} e^5 - \frac{33}{64} e^4 + \frac{887}{4} e^3 - \frac{1603}{8} e^2 - \frac{6169}{4} e + \frac{10067}{4}$ |
| 19 | $[19, 19, -w^3 + 3 w - 1]$ | $-\frac{1}{8} e^7 - \frac{3}{16} e^6 + \frac{121}{16} e^5 + \frac{37}{16} e^4 - \frac{2495}{16} e^3 + \frac{909}{8} e^2 + \frac{4303}{4} e - \frac{3299}{2}$ |
| 43 | $[43, 43, -w^2 + w - 1]$ | $\phantom{-}\frac{3}{32} e^7 + \frac{3}{32} e^6 - \frac{189}{32} e^5 + \frac{13}{32} e^4 + \frac{2003}{16} e^3 - \frac{963}{8} e^2 - \frac{3517}{4} e + 1451$ |
| 43 | $[43, 43, w^2 + w + 1]$ | $-\frac{11}{64} e^7 - \frac{13}{64} e^6 + \frac{679}{64} e^5 + \frac{33}{64} e^4 - \frac{887}{4} e^3 + \frac{1595}{8} e^2 + \frac{6165}{4} e - \frac{9995}{4}$ |
| 49 | $[49, 7, w^3 + w^2 - 6 w - 3]$ | $\phantom{-}\frac{3}{16} e^7 + \frac{3}{16} e^6 - \frac{189}{16} e^5 + \frac{13}{16} e^4 + \frac{2003}{8} e^3 - \frac{967}{4} e^2 - \frac{3515}{2} e + 2918$ |
| 49 | $[49, 7, w^3 - w^2 - 6 w + 3]$ | $-\frac{1}{4} e^7 - \frac{3}{8} e^6 + \frac{121}{8} e^5 + \frac{35}{8} e^4 - \frac{2499}{8} e^3 + 236 e^2 + \frac{4321}{2} e - 3370$ |
| 53 | $[53, 53, 2 w^3 - w^2 - 9 w + 3]$ | $-e^2 - 2 e + 22$ |
| 53 | $[53, 53, 2 w^3 + w^2 - 9 w - 3]$ | $\phantom{-}\frac{1}{32} e^7 + \frac{3}{32} e^6 - \frac{53}{32} e^5 - \frac{87}{32} e^4 + \frac{123}{4} e^3 + \frac{31}{4} e^2 - \frac{393}{2} e + \frac{369}{2}$ |
| 59 | $[59, 59, w^3 - w^2 - 4 w + 1]$ | $-\frac{1}{16} e^6 - \frac{5}{16} e^5 + \frac{43}{16} e^4 + \frac{173}{16} e^3 - \frac{327}{8} e^2 - \frac{369}{4} e + \frac{473}{2}$ |
| 59 | $[59, 59, -w^3 - w^2 + 4 w + 1]$ | $-\frac{3}{32} e^7 - \frac{3}{32} e^6 + \frac{189}{32} e^5 - \frac{13}{32} e^4 - \frac{2003}{16} e^3 + \frac{963}{8} e^2 + \frac{3509}{4} e - 1447$ |
| 67 | $[67, 67, 3 w^3 - 13 w + 1]$ | $\phantom{-}\frac{1}{16} e^6 + \frac{5}{16} e^5 - \frac{43}{16} e^4 - \frac{173}{16} e^3 + \frac{327}{8} e^2 + \frac{369}{4} e - \frac{473}{2}$ |
| 67 | $[67, 67, -w^3 + w^2 + 6 w - 5]$ | $\phantom{-}\frac{3}{32} e^7 + \frac{3}{32} e^6 - \frac{189}{32} e^5 + \frac{13}{32} e^4 + \frac{2003}{16} e^3 - \frac{971}{8} e^2 - \frac{3513}{4} e + 1465$ |
| 81 | $[81, 3, -3]$ | $-\frac{3}{16} e^7 - \frac{3}{16} e^6 + \frac{189}{16} e^5 - \frac{13}{16} e^4 - \frac{2003}{8} e^3 + \frac{967}{4} e^2 + \frac{3515}{2} e - 2914$ |
| 83 | $[83, 83, -2 w^3 - w^2 + 9 w + 7]$ | $\phantom{-}\frac{1}{8} e^7 + \frac{3}{16} e^6 - \frac{121}{16} e^5 - \frac{37}{16} e^4 + \frac{2495}{16} e^3 - \frac{917}{8} e^2 - \frac{4315}{4} e + \frac{3343}{2}$ |
| 83 | $[83, 83, 4 w^3 - 18 w - 1]$ | $\phantom{-}\frac{17}{64} e^7 + \frac{15}{64} e^6 - \frac{1077}{64} e^5 + \frac{165}{64} e^4 + \frac{1429}{4} e^3 - \frac{2897}{8} e^2 - \frac{10011}{4} e + \frac{16801}{4}$ |
| 89 | $[89, 89, -2 w^3 + 10 w + 1]$ | $\phantom{-}\frac{7}{32} e^7 + \frac{9}{32} e^6 - \frac{431}{32} e^5 - \frac{61}{32} e^4 + \frac{2249}{8} e^3 - 234 e^2 - 1955 e + \frac{6205}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w + 1]$ | $-1$ |
| $13$ | $[13,13,w^2 - w - 3]$ | $-1$ |