Properties

Label 4.4.11197.1-21.1-f
Base field 4.4.11197.1
Weight $[2, 2, 2, 2]$
Level norm $21$
Level $[21, 21, w^{3} - w^{2} - 5w]$
Dimension $5$
CM no
Base change no

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Base field 4.4.11197.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 3x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[21, 21, w^{3} - w^{2} - 5w]$
Dimension: $5$
CM: no
Base change: no
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{5} - 5x^{4} - 18x^{3} + 78x^{2} + 89x - 257\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $-1$
7 $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ $-1$
11 $[11, 11, -w - 2]$ $\phantom{-}e$
11 $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}e - 3$
13 $[13, 13, -w^{2} + 2w + 2]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{5}{4}e^{2} - \frac{9}{4}e + \frac{45}{4}$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{8}e^{4} - \frac{3}{4}e^{3} - e^{2} + \frac{29}{4}e + \frac{3}{8}$
19 $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{7}{4}e^{2} - \frac{5}{4}e + \frac{51}{4}$
23 $[23, 23, -w^{2} + w + 3]$ $-\frac{1}{4}e^{3} + \frac{3}{4}e^{2} + \frac{13}{4}e - \frac{27}{4}$
23 $[23, 23, -w^{2} + 3]$ $-\frac{1}{4}e^{3} + \frac{3}{4}e^{2} + \frac{17}{4}e - \frac{23}{4}$
27 $[27, 3, w^{3} - 3w^{2} - w + 4]$ $\phantom{-}\frac{1}{8}e^{4} - e^{3} + \frac{1}{4}e^{2} + \frac{19}{2}e - \frac{55}{8}$
29 $[29, 29, -w^{3} + 3w^{2} + 3w - 5]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{3}{4}e^{2} - \frac{13}{4}e + \frac{7}{4}$
29 $[29, 29, w^{3} - 2w^{2} - 4w]$ $-\frac{1}{8}e^{4} + \frac{3}{4}e^{3} - \frac{21}{4}e + \frac{69}{8}$
47 $[47, 47, -w^{3} + 2w^{2} + 3w - 5]$ $-\frac{1}{4}e^{4} + \frac{5}{4}e^{3} + \frac{9}{4}e^{2} - \frac{41}{4}e + 1$
47 $[47, 47, w^{2} - 3w - 2]$ $\phantom{-}e^{2} - e - 12$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $-\frac{1}{8}e^{4} + \frac{1}{2}e^{3} + \frac{9}{4}e^{2} - 5e - \frac{77}{8}$
67 $[67, 67, -w^{3} + w^{2} + 5w - 1]$ $-\frac{1}{8}e^{4} + \frac{1}{2}e^{3} + \frac{5}{4}e^{2} - 5e + \frac{59}{8}$
67 $[67, 67, -2w^{3} + 3w^{2} + 11w - 7]$ $\phantom{-}\frac{1}{4}e^{4} - e^{3} - \frac{7}{2}e^{2} + 9e + \frac{37}{4}$
83 $[83, 83, -2w + 3]$ $\phantom{-}\frac{3}{4}e^{3} - \frac{13}{4}e^{2} - \frac{31}{4}e + \frac{105}{4}$
89 $[89, 89, 3w^{3} - 7w^{2} - 9w + 9]$ $-\frac{3}{4}e^{3} + \frac{13}{4}e^{2} + \frac{31}{4}e - \frac{101}{4}$
97 $[97, 97, w^{3} - w^{2} - 4w - 3]$ $-\frac{1}{8}e^{4} + e^{3} - \frac{1}{4}e^{2} - \frac{13}{2}e + \frac{47}{8}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 1]$ $1$
$7$ $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ $1$