Properties

Label 4.4.19796.1-1.1-b
Base field 4.4.19796.1
Weight $[2, 2, 2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $6$
CM no
Base change no

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Base field 4.4.19796.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 8\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[1, 1, 1]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 32x^{4} + 304x^{2} - 736\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + 2]$ $\phantom{-}\frac{1}{8}e^{4} - \frac{5}{2}e^{2} + 9$
2 $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ $\phantom{-}\frac{1}{8}e^{4} - 2e^{2} + 4$
5 $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ $\phantom{-}e$
13 $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ $-\frac{1}{8}e^{5} + 2e^{3} - 3e$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{5}{2}e^{3} + 9e$
19 $[19, 19, -w^{3} + 3w^{2} + 2w - 7]$ $\phantom{-}\frac{1}{2}e^{3} - 6e$
23 $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{9}{2}e^{2} + 18$
31 $[31, 31, -w^{2} + w + 1]$ $-\frac{1}{2}e^{3} + 6e$
47 $[47, 47, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}\frac{1}{4}e^{5} - 5e^{3} + 20e$
49 $[49, 7, 2w^{3} - 5w^{2} - 7w + 11]$ $-\frac{1}{4}e^{5} + 5e^{3} - 21e$
53 $[53, 53, -3w^{3} + 9w^{2} + 10w - 31]$ $-\frac{1}{2}e^{4} + \frac{17}{2}e^{2} - 20$
53 $[53, 53, w^{3} - w^{2} - 4w + 1]$ $-\frac{1}{4}e^{4} + 5e^{2} - 10$
61 $[61, 61, 3w^{3} - 6w^{2} - 13w + 13]$ $-\frac{1}{8}e^{5} + \frac{5}{2}e^{3} - 13e$
61 $[61, 61, 2w^{2} - 7]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{9}{2}e^{3} + 13e$
71 $[71, 71, w^{2} - 3w - 5]$ $-\frac{3}{4}e^{4} + \frac{29}{2}e^{2} - 50$
73 $[73, 73, 2w - 3]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{9}{2}e^{3} + 15e$
73 $[73, 73, -2w^{3} + 6w^{2} + 6w - 19]$ $-\frac{1}{8}e^{5} + \frac{5}{2}e^{3} - 11e$
79 $[79, 79, 2w^{2} - 5]$ $\phantom{-}\frac{3}{4}e^{4} - \frac{29}{2}e^{2} + 46$
81 $[81, 3, -3]$ $-\frac{3}{4}e^{4} + 13e^{2} - 38$
101 $[101, 101, 2w^{2} - 4w - 9]$ $-\frac{3}{8}e^{5} + \frac{13}{2}e^{3} - 17e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).