Properties

Label 4.4.16997.1-25.1-j
Base field 4.4.16997.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, -w^{3} + 4w]$
Dimension $7$
CM no
Base change no

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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 $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ $-\frac{171}{1012}e^{6} + \frac{81}{253}e^{5} + \frac{1392}{253}e^{4} - \frac{2460}{253}e^{3} - \frac{33595}{1012}e^{2} + \frac{5659}{253}e + \frac{14703}{506}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w]$ $1$
$5$ $[5, 5, -w^{2} + w + 2]$ $-1$