Properties

Label 4.4.725.1-281.1-b
Base field 4.4.725.1
Weight $[2, 2, 2, 2]$
Level norm $281$
Level $[281, 281, -3w^{3} + w^{2} + 11w - 1]$
Dimension $4$
CM no
Base change no

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Base field 4.4.725.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[281, 281, -3w^{3} + w^{2} + 11w - 1]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $5$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 4x^{3} - 24x^{2} + 64x + 144\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -w^{3} + 2w^{2} + w - 3]$ $\phantom{-}\frac{1}{8}e^{3} - \frac{1}{4}e^{2} - \frac{5}{2}e + 3$
11 $[11, 11, w^{3} - 3w]$ $\phantom{-}e$
16 $[16, 2, 2]$ $-\frac{1}{4}e^{2} + 6$
19 $[19, 19, -w^{3} + 2w + 2]$ $-\frac{1}{4}e^{3} + \frac{1}{2}e^{2} + \frac{9}{2}e - 3$
19 $[19, 19, 2w^{3} - 3w^{2} - 4w + 2]$ $-\frac{1}{8}e^{3} - \frac{1}{4}e^{2} + \frac{5}{2}e + 7$
25 $[25, 5, 2w^{3} - 2w^{2} - 4w + 1]$ $-\frac{1}{4}e^{2} + e + 3$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{2}e^{2} - 4e$
31 $[31, 31, w^{3} - 4w + 1]$ $\phantom{-}\frac{1}{8}e^{3} + \frac{3}{4}e^{2} - \frac{7}{2}e - 15$
31 $[31, 31, -w^{2} + 2w + 3]$ $\phantom{-}\frac{1}{8}e^{3} + \frac{5}{4}e^{2} - 5e - 22$
41 $[41, 41, 2w^{2} - w - 3]$ $\phantom{-}\frac{1}{2}e^{2} - 2e - 6$
41 $[41, 41, -w^{3} + 3w^{2} + w - 4]$ $-\frac{1}{2}e^{2} + e + 8$
49 $[49, 7, 2w^{3} - 3w^{2} - 5w + 2]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{3}{4}e^{2} - 4e + 9$
49 $[49, 7, w^{2} + w - 3]$ $-\frac{1}{4}e^{3} + \frac{3}{4}e^{2} + 4e - 3$
61 $[61, 61, 2w^{3} - 3w^{2} - 4w]$ $-\frac{1}{4}e^{3} + \frac{1}{2}e^{2} + 4e - 2$
61 $[61, 61, -3w^{3} + 4w^{2} + 7w - 3]$ $-\frac{3}{8}e^{3} - \frac{3}{4}e^{2} + \frac{15}{2}e + 23$
79 $[79, 79, 2w^{3} - 4w^{2} - 3w + 2]$ $-\frac{1}{4}e^{3} - e^{2} + 6e + 20$
79 $[79, 79, w^{3} + w^{2} - 3w - 5]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{5}{2}e - 9$
81 $[81, 3, -3]$ $-\frac{3}{8}e^{3} + \frac{1}{4}e^{2} + \frac{13}{2}e + 5$
89 $[89, 89, -3w^{3} + 4w^{2} + 5w - 3]$ $-\frac{1}{4}e^{3} - \frac{1}{2}e^{2} + \frac{11}{2}e + 11$
89 $[89, 89, 3w^{3} - 2w^{2} - 7w]$ $-\frac{1}{4}e^{3} + e^{2} + \frac{9}{2}e - 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$281$ $[281, 281, -3w^{3} + w^{2} + 11w - 1]$ $1$