Base field 5.5.160801.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[27, 3, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 6x^{6} - 28x^{5} + 182x^{4} + 40x^{3} - 664x^{2} + 288x - 32\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $-1$ |
| 9 | $[9, 3, -w^{4} + 5w^{2} - 3]$ | $\phantom{-}1$ |
| 9 | $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $\phantom{-}\frac{3}{32}e^{6} - \frac{9}{16}e^{5} - \frac{11}{4}e^{4} + \frac{273}{16}e^{3} + \frac{31}{4}e^{2} - 62e + \frac{27}{2}$ |
| 17 | $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $\phantom{-}\frac{3}{32}e^{6} - \frac{9}{16}e^{5} - \frac{11}{4}e^{4} + \frac{273}{16}e^{3} + \frac{31}{4}e^{2} - 62e + \frac{27}{2}$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w - 2]$ | $\phantom{-}\frac{3}{16}e^{6} - \frac{17}{16}e^{5} - \frac{11}{2}e^{4} + \frac{257}{8}e^{3} + \frac{119}{8}e^{2} - \frac{461}{4}e + \frac{55}{2}$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-\frac{9}{32}e^{6} + \frac{13}{8}e^{5} + \frac{33}{4}e^{4} - \frac{787}{16}e^{3} - \frac{181}{8}e^{2} + \frac{709}{4}e - 39$ |
| 31 | $[31, 31, w^{3} - 4w + 2]$ | $-\frac{21}{32}e^{6} + \frac{61}{16}e^{5} + \frac{77}{4}e^{4} - \frac{1855}{16}e^{3} - 53e^{2} + \frac{859}{2}e - \frac{183}{2}$ |
| 32 | $[32, 2, 2]$ | $-\frac{29}{64}e^{6} + \frac{41}{16}e^{5} + \frac{107}{8}e^{4} - \frac{2487}{32}e^{3} - \frac{617}{16}e^{2} + \frac{2273}{8}e - \frac{117}{2}$ |
| 37 | $[37, 37, w^{3} - 3w - 1]$ | $\phantom{-}\frac{27}{32}e^{6} - \frac{39}{8}e^{5} - \frac{99}{4}e^{4} + \frac{2369}{16}e^{3} + \frac{543}{8}e^{2} - \frac{2179}{4}e + 117$ |
| 53 | $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ | $-\frac{3}{16}e^{6} + \frac{17}{16}e^{5} + \frac{11}{2}e^{4} - \frac{257}{8}e^{3} - \frac{119}{8}e^{2} + \frac{461}{4}e - \frac{51}{2}$ |
| 59 | $[59, 59, -w^{4} + 5w^{2} + w - 4]$ | $\phantom{-}\frac{1}{32}e^{5} - \frac{5}{4}e^{3} + \frac{3}{16}e^{2} + \frac{75}{8}e - \frac{7}{4}$ |
| 61 | $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ | $-\frac{1}{8}e^{6} + \frac{3}{4}e^{5} + \frac{7}{2}e^{4} - \frac{91}{4}e^{3} - 5e^{2} + 83e - 26$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ | $\phantom{-}\frac{1}{32}e^{6} - \frac{1}{4}e^{5} - \frac{3}{4}e^{4} + \frac{123}{16}e^{3} - \frac{17}{8}e^{2} - \frac{115}{4}e + 18$ |
| 71 | $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ | $-\frac{21}{32}e^{6} + \frac{61}{16}e^{5} + \frac{77}{4}e^{4} - \frac{1855}{16}e^{3} - 53e^{2} + \frac{857}{2}e - \frac{187}{2}$ |
| 79 | $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ | $-\frac{11}{32}e^{6} + \frac{63}{32}e^{5} + \frac{41}{4}e^{4} - \frac{957}{16}e^{3} - \frac{517}{16}e^{2} + \frac{1767}{8}e - \frac{161}{4}$ |
| 83 | $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ | $\phantom{-}\frac{1}{32}e^{6} - \frac{1}{4}e^{5} - \frac{3}{4}e^{4} + \frac{123}{16}e^{3} - \frac{17}{8}e^{2} - \frac{115}{4}e + 14$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ | $\phantom{-}\frac{7}{32}e^{6} - \frac{5}{4}e^{5} - \frac{25}{4}e^{4} + \frac{605}{16}e^{3} + \frac{105}{8}e^{2} - \frac{553}{4}e + 36$ |
| 83 | $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ | $\phantom{-}\frac{33}{32}e^{6} - \frac{191}{32}e^{5} - \frac{121}{4}e^{4} + \frac{2903}{16}e^{3} + \frac{1321}{16}e^{2} - \frac{5371}{8}e + \frac{609}{4}$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ | $\phantom{-}\frac{25}{32}e^{6} - \frac{73}{16}e^{5} - \frac{91}{4}e^{4} + \frac{2219}{16}e^{3} + 58e^{2} - \frac{1021}{2}e + \frac{239}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $1$ |
| $9$ | $[9, 3, -w^{4} + 5w^{2} - 3]$ | $-1$ |