Properties

Label 4.4.8768.1-28.2-d
Base field 4.4.8768.1
Weight $[2, 2, 2, 2]$
Level norm $28$
Level $[28, 14, -w^{3} + 3w^{2} + w - 4]$
Dimension $4$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 4.4.8768.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 6x + 7\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[28, 14, -w^{3} + 3w^{2} + w - 4]$
Dimension: $4$
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:

\(x^{4} - 4x^{3} - 13x^{2} + 34x + 71\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $-1$
7 $[7, 7, w]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 2w + 1]$ $-1$
7 $[7, 7, w^{2} - 2]$ $\phantom{-}e^{3} - \frac{5}{2}e^{2} - \frac{15}{2}e + \frac{7}{2}$
7 $[7, 7, w - 1]$ $-\frac{1}{2}e^{2} + \frac{1}{2}e + \frac{13}{2}$
23 $[23, 23, -w^{3} + w^{2} + 3w - 1]$ $-\frac{1}{2}e^{3} - e^{2} + 9e + \frac{35}{2}$
23 $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - \frac{19}{2}e - 21$
31 $[31, 31, w^{2} - 5]$ $\phantom{-}\frac{9}{2}e^{2} - \frac{19}{2}e - \frac{75}{2}$
31 $[31, 31, -w^{2} + 2w + 4]$ $-e^{3} + \frac{3}{2}e^{2} + \frac{17}{2}e + \frac{15}{2}$
41 $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ $-e^{2} + e + 9$
41 $[41, 41, w^{3} - w^{2} - 3w - 3]$ $\phantom{-}e^{3} - 3e^{2} - 6e + 14$
47 $[47, 47, w^{2} - 2w - 5]$ $-\frac{1}{2}e^{3} + \frac{13}{2}e^{2} - \frac{17}{2}e - 45$
47 $[47, 47, w^{2} - 6]$ $-\frac{1}{2}e^{3} + 2e^{2} + 3e - \frac{3}{2}$
71 $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ $-2e^{3} + 3e^{2} + 19e + 11$
71 $[71, 71, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}e^{3} - 7e^{2} + 3e + 44$
79 $[79, 79, -w - 3]$ $-\frac{1}{2}e^{3} + \frac{23}{2}e^{2} - \frac{35}{2}e - 89$
79 $[79, 79, w - 4]$ $\phantom{-}e^{3} - 7e^{2} + 2e + 39$
81 $[81, 3, -3]$ $-\frac{1}{2}e^{3} + e^{2} + 3e - \frac{9}{2}$
89 $[89, 89, w^{2} - 3w - 2]$ $-\frac{1}{2}e^{3} + e^{2} + 4e + \frac{15}{2}$
89 $[89, 89, w^{2} + w - 4]$ $\phantom{-}3e^{3} - 12e^{2} - 13e + 52$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -w^{2} + w + 3]$ $1$
$7$ $[7, 7, -w^{2} + 2w + 1]$ $1$