Base field 4.4.16997.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, -w^{3} + 4w]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $39$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 3x^{6} - 30x^{5} + 94x^{4} + 119x^{3} - 345x^{2} + 22x + 134\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w]$ | $-1$ |
| 5 | $[5, 5, -w^{2} + w + 2]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $\phantom{-}\frac{57}{1012}e^{6} - \frac{27}{253}e^{5} - \frac{464}{253}e^{4} + \frac{820}{253}e^{3} + \frac{10861}{1012}e^{2} - \frac{2055}{253}e - \frac{2371}{506}$ |
| 13 | $[13, 13, w^{2} - w - 4]$ | $-\frac{101}{3542}e^{6} + \frac{109}{1771}e^{5} + \frac{3231}{3542}e^{4} - \frac{3554}{1771}e^{3} - \frac{9132}{1771}e^{2} + \frac{12569}{1771}e + \frac{1436}{1771}$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{197}{7084}e^{6} - \frac{80}{1771}e^{5} - \frac{3265}{3542}e^{4} + \frac{2186}{1771}e^{3} + \frac{39499}{7084}e^{2} - \frac{45}{1771}e - \frac{10183}{3542}$ |
| 19 | $[19, 19, -w^{2} + w + 1]$ | $-\frac{85}{3542}e^{6} + \frac{201}{3542}e^{5} + \frac{1193}{1771}e^{4} - \frac{6245}{3542}e^{3} - \frac{6165}{3542}e^{2} + \frac{7860}{1771}e - \frac{5630}{1771}$ |
| 23 | $[23, 23, -w^{3} + 4w + 2]$ | $-\frac{569}{7084}e^{6} + \frac{579}{3542}e^{5} + \frac{4441}{1771}e^{4} - \frac{17725}{3542}e^{3} - \frac{88357}{7084}e^{2} + \frac{20474}{1771}e + \frac{8879}{3542}$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 3w - 1]$ | $\phantom{-}\frac{181}{1771}e^{6} - \frac{303}{1771}e^{5} - \frac{5685}{1771}e^{4} + \frac{9652}{1771}e^{3} + \frac{30942}{1771}e^{2} - \frac{22640}{1771}e - \frac{23944}{1771}$ |
| 29 | $[29, 29, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}\frac{181}{1771}e^{6} - \frac{303}{1771}e^{5} - \frac{5685}{1771}e^{4} + \frac{9652}{1771}e^{3} + \frac{30942}{1771}e^{2} - \frac{24411}{1771}e - \frac{18631}{1771}$ |
| 29 | $[29, 29, -w + 3]$ | $\phantom{-}\frac{31}{1012}e^{6} - \frac{28}{253}e^{5} - \frac{447}{506}e^{4} + \frac{841}{253}e^{3} + \frac{2933}{1012}e^{2} - \frac{2609}{253}e - \frac{819}{506}$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 5w - 2]$ | $-\frac{8}{161}e^{6} + \frac{17}{322}e^{5} + \frac{523}{322}e^{4} - \frac{541}{322}e^{3} - \frac{3405}{322}e^{2} + \frac{201}{161}e + \frac{1270}{161}$ |
| 37 | $[37, 37, w^{3} - 4w - 1]$ | $-\frac{601}{7084}e^{6} + \frac{298}{1771}e^{5} + \frac{9727}{3542}e^{4} - \frac{9294}{1771}e^{3} - \frac{112555}{7084}e^{2} + \frac{23412}{1771}e + \frac{30095}{3542}$ |
| 37 | $[37, 37, w^{3} - 3w + 1]$ | $-\frac{383}{3542}e^{6} + \frac{739}{3542}e^{5} + \frac{12147}{3542}e^{4} - \frac{22097}{3542}e^{3} - \frac{33735}{1771}e^{2} + \frac{18748}{1771}e + \frac{25470}{1771}$ |
| 53 | $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ | $-\frac{27}{7084}e^{6} - \frac{41}{3542}e^{5} + \frac{879}{3542}e^{4} + \frac{1873}{3542}e^{3} - \frac{27169}{7084}e^{2} - \frac{7815}{1771}e + \frac{7275}{3542}$ |
| 59 | $[59, 59, w^{2} + w - 4]$ | $-\frac{135}{7084}e^{6} - \frac{205}{3542}e^{5} + \frac{1312}{1771}e^{4} + \frac{5823}{3542}e^{3} - \frac{54379}{7084}e^{2} - \frac{12510}{1771}e + \frac{22207}{3542}$ |
| 61 | $[61, 61, -2w^{2} + w + 8]$ | $-\frac{63}{1012}e^{6} + \frac{73}{506}e^{5} + \frac{1039}{506}e^{4} - \frac{2039}{506}e^{3} - \frac{12457}{1012}e^{2} + \frac{1499}{253}e + \frac{4325}{506}$ |
| 73 | $[73, 73, -w^{3} + 5w - 1]$ | $-\frac{643}{7084}e^{6} + \frac{729}{3542}e^{5} + \frac{5252}{1771}e^{4} - \frac{21381}{3542}e^{3} - \frac{123727}{7084}e^{2} + \frac{24833}{1771}e + \frac{47315}{3542}$ |
| 79 | $[79, 79, 2w^{2} + w - 6]$ | $-\frac{13}{1012}e^{6} - \frac{1}{506}e^{5} + \frac{57}{253}e^{4} + \frac{21}{506}e^{3} + \frac{1855}{1012}e^{2} - \frac{1289}{253}e - \frac{4537}{506}$ |
| 79 | $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ | $-\frac{171}{1012}e^{6} + \frac{81}{253}e^{5} + \frac{1392}{253}e^{4} - \frac{2460}{253}e^{3} - \frac{33595}{1012}e^{2} + \frac{5659}{253}e + \frac{14703}{506}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w]$ | $1$ |
| $5$ | $[5, 5, -w^{2} + w + 2]$ | $-1$ |