Base field 4.4.9248.1
Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} + 2\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[26, 26, -w^{3} + 4w - 3]$ |
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:
\(x^{8} + 3x^{7} - 67x^{6} - 255x^{5} + 1318x^{4} + 6568x^{3} - 4288x^{2} - 52336x - 60832\) |
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 | $[2, 2, w + 1]$ | $-1$ |
13 | $[13, 13, -w^{2} + w + 3]$ | $\phantom{-}e$ |
13 | $[13, 13, w^{2} + w - 3]$ | $-1$ |
19 | $[19, 19, -w^{3} + 3w + 1]$ | $-\frac{1}{8}e^{7} + \frac{3}{16}e^{6} + \frac{121}{16}e^{5} - \frac{37}{16}e^{4} - \frac{2495}{16}e^{3} - \frac{909}{8}e^{2} + \frac{4303}{4}e + \frac{3299}{2}$ |
19 | $[19, 19, -w^{3} + 3w - 1]$ | $\phantom{-}\frac{11}{64}e^{7} - \frac{13}{64}e^{6} - \frac{679}{64}e^{5} + \frac{33}{64}e^{4} + \frac{887}{4}e^{3} + \frac{1603}{8}e^{2} - \frac{6169}{4}e - \frac{10067}{4}$ |
43 | $[43, 43, -w^{2} + w - 1]$ | $\phantom{-}\frac{11}{64}e^{7} - \frac{13}{64}e^{6} - \frac{679}{64}e^{5} + \frac{33}{64}e^{4} + \frac{887}{4}e^{3} + \frac{1595}{8}e^{2} - \frac{6165}{4}e - \frac{9995}{4}$ |
43 | $[43, 43, w^{2} + w + 1]$ | $-\frac{3}{32}e^{7} + \frac{3}{32}e^{6} + \frac{189}{32}e^{5} + \frac{13}{32}e^{4} - \frac{2003}{16}e^{3} - \frac{963}{8}e^{2} + \frac{3517}{4}e + 1451$ |
49 | $[49, 7, w^{3} + w^{2} - 6w - 3]$ | $-\frac{1}{4}e^{7} + \frac{3}{8}e^{6} + \frac{121}{8}e^{5} - \frac{35}{8}e^{4} - \frac{2499}{8}e^{3} - 236e^{2} + \frac{4321}{2}e + 3370$ |
49 | $[49, 7, w^{3} - w^{2} - 6w + 3]$ | $\phantom{-}\frac{3}{16}e^{7} - \frac{3}{16}e^{6} - \frac{189}{16}e^{5} - \frac{13}{16}e^{4} + \frac{2003}{8}e^{3} + \frac{967}{4}e^{2} - \frac{3515}{2}e - 2918$ |
53 | $[53, 53, 2w^{3} - w^{2} - 9w + 3]$ | $-\frac{1}{32}e^{7} + \frac{3}{32}e^{6} + \frac{53}{32}e^{5} - \frac{87}{32}e^{4} - \frac{123}{4}e^{3} + \frac{31}{4}e^{2} + \frac{393}{2}e + \frac{369}{2}$ |
53 | $[53, 53, 2w^{3} + w^{2} - 9w - 3]$ | $-e^{2} + 2e + 22$ |
59 | $[59, 59, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}\frac{3}{32}e^{7} - \frac{3}{32}e^{6} - \frac{189}{32}e^{5} - \frac{13}{32}e^{4} + \frac{2003}{16}e^{3} + \frac{963}{8}e^{2} - \frac{3509}{4}e - 1447$ |
59 | $[59, 59, -w^{3} - w^{2} + 4w + 1]$ | $-\frac{1}{16}e^{6} + \frac{5}{16}e^{5} + \frac{43}{16}e^{4} - \frac{173}{16}e^{3} - \frac{327}{8}e^{2} + \frac{369}{4}e + \frac{473}{2}$ |
67 | $[67, 67, 3w^{3} - 13w + 1]$ | $\phantom{-}\frac{3}{32}e^{7} - \frac{3}{32}e^{6} - \frac{189}{32}e^{5} - \frac{13}{32}e^{4} + \frac{2003}{16}e^{3} + \frac{971}{8}e^{2} - \frac{3513}{4}e - 1465$ |
67 | $[67, 67, -w^{3} + w^{2} + 6w - 5]$ | $-\frac{1}{16}e^{6} + \frac{5}{16}e^{5} + \frac{43}{16}e^{4} - \frac{173}{16}e^{3} - \frac{327}{8}e^{2} + \frac{369}{4}e + \frac{473}{2}$ |
81 | $[81, 3, -3]$ | $\phantom{-}\frac{3}{16}e^{7} - \frac{3}{16}e^{6} - \frac{189}{16}e^{5} - \frac{13}{16}e^{4} + \frac{2003}{8}e^{3} + \frac{967}{4}e^{2} - \frac{3515}{2}e - 2914$ |
83 | $[83, 83, -2w^{3} - w^{2} + 9w + 7]$ | $-\frac{17}{64}e^{7} + \frac{15}{64}e^{6} + \frac{1077}{64}e^{5} + \frac{165}{64}e^{4} - \frac{1429}{4}e^{3} - \frac{2897}{8}e^{2} + \frac{10011}{4}e + \frac{16801}{4}$ |
83 | $[83, 83, 4w^{3} - 18w - 1]$ | $-\frac{1}{8}e^{7} + \frac{3}{16}e^{6} + \frac{121}{16}e^{5} - \frac{37}{16}e^{4} - \frac{2495}{16}e^{3} - \frac{917}{8}e^{2} + \frac{4315}{4}e + \frac{3343}{2}$ |
89 | $[89, 89, -2w^{3} + 10w + 1]$ | $\phantom{-}\frac{5}{32}e^{7} - \frac{7}{32}e^{6} - \frac{305}{32}e^{5} + \frac{67}{32}e^{4} + \frac{395}{2}e^{3} + 158e^{2} - \frac{2731}{2}e - \frac{4339}{2}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,w+1]$ | $1$ |
$13$ | $[13,13,w^{2}+w-3]$ | $1$ |