Base field 4.4.14013.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 6x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 17x^{8} + 86x^{6} - 130x^{4} + 64x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}\frac{1}{4}e^{8} - \frac{17}{4}e^{6} + \frac{43}{2}e^{4} - \frac{63}{2}e^{2} + 10$ |
| 7 | $[7, 7, -w^{3} + 5w - 2]$ | $-\frac{1}{4}e^{9} + \frac{17}{4}e^{7} - \frac{43}{2}e^{5} + \frac{65}{2}e^{3} - 16e$ |
| 13 | $[13, 13, -w^{3} + 5w + 1]$ | $\phantom{-}\frac{5}{4}e^{9} - \frac{83}{4}e^{7} + 99e^{5} - \frac{243}{2}e^{3} + 33e$ |
| 16 | $[16, 2, 2]$ | $-1$ |
| 29 | $[29, 29, w^{3} + w^{2} - 5w - 1]$ | $\phantom{-}\frac{9}{8}e^{9} - \frac{147}{8}e^{7} + \frac{169}{2}e^{5} - \frac{365}{4}e^{3} + \frac{41}{2}e$ |
| 31 | $[31, 31, -w^{3} + 4w - 1]$ | $\phantom{-}\frac{1}{4}e^{9} - \frac{17}{4}e^{7} + \frac{43}{2}e^{5} - \frac{63}{2}e^{3} + 10e$ |
| 41 | $[41, 41, w^{3} - 6w + 1]$ | $\phantom{-}\frac{3}{4}e^{9} - \frac{49}{4}e^{7} + 56e^{5} - \frac{113}{2}e^{3} + 4e$ |
| 43 | $[43, 43, w^{3} + w^{2} - 6w - 1]$ | $\phantom{-}\frac{3}{8}e^{9} - \frac{49}{8}e^{7} + \frac{57}{2}e^{5} - \frac{135}{4}e^{3} + \frac{29}{2}e$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + 5w - 11]$ | $\phantom{-}\frac{5}{4}e^{8} - \frac{81}{4}e^{6} + \frac{185}{2}e^{4} - \frac{203}{2}e^{2} + 28$ |
| 49 | $[49, 7, w^{2} + w - 1]$ | $\phantom{-}\frac{3}{2}e^{9} - 25e^{7} + \frac{241}{2}e^{5} - 153e^{3} + 44e$ |
| 59 | $[59, 59, w^{3} - w^{2} - 6w + 4]$ | $\phantom{-}\frac{1}{4}e^{9} - \frac{19}{4}e^{7} + 29e^{5} - \frac{123}{2}e^{3} + 30e$ |
| 59 | $[59, 59, w^{2} - w - 4]$ | $-\frac{5}{4}e^{8} + \frac{81}{4}e^{6} - \frac{183}{2}e^{4} + \frac{183}{2}e^{2} - 16$ |
| 67 | $[67, 67, 2w^{3} + w^{2} - 9w - 2]$ | $-\frac{5}{8}e^{9} + \frac{87}{8}e^{7} - \frac{115}{2}e^{5} + \frac{385}{4}e^{3} - \frac{103}{2}e$ |
| 71 | $[71, 71, -3w^{3} - w^{2} + 16w + 5]$ | $-\frac{17}{8}e^{9} + \frac{279}{8}e^{7} - 163e^{5} + \frac{757}{4}e^{3} - \frac{95}{2}e$ |
| 71 | $[71, 71, 2w - 1]$ | $\phantom{-}\frac{1}{8}e^{9} - \frac{19}{8}e^{7} + \frac{29}{2}e^{5} - \frac{125}{4}e^{3} + \frac{33}{2}e$ |
| 73 | $[73, 73, w^{3} - 6w + 4]$ | $\phantom{-}\frac{5}{4}e^{9} - \frac{81}{4}e^{7} + \frac{183}{2}e^{5} - \frac{185}{2}e^{3} + 17e$ |
| 83 | $[83, 83, w^{3} - w^{2} - 3w + 4]$ | $\phantom{-}\frac{3}{4}e^{8} - \frac{49}{4}e^{6} + 55e^{4} - \frac{99}{2}e^{2} + 9$ |
| 103 | $[103, 103, w^{3} + w^{2} - 4w - 5]$ | $-\frac{3}{2}e^{8} + 24e^{6} - \frac{211}{2}e^{4} + 96e^{2} - 9$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $16$ | $[16, 2, 2]$ | $1$ |