Properties

Label 4.4.9301.1-7.2-b
Base field 4.4.9301.1
Weight $[2, 2, 2, 2]$
Level norm $7$
Level $[7, 7, -w^{2} + w + 2]$
Dimension $4$
CM no
Base change no

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Base field 4.4.9301.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[7, 7, -w^{2} + w + 2]$
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:

\(x^{4} - 3x^{3} - 4x^{2} + 8x + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
5 $[5, 5, -w^{3} + w^{2} + 4w + 1]$ $-e^{2} + 2e + 2$
7 $[7, 7, -w^{2} + 2]$ $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + 2e - 2$
7 $[7, 7, -w^{2} + w + 2]$ $-1$
16 $[16, 2, 2]$ $-e - 1$
17 $[17, 17, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}2e - 2$
23 $[23, 23, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} + 4$
27 $[27, 3, -w^{3} + w^{2} + 5w - 1]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{7}{2}e^{2} + 2e + 8$
37 $[37, 37, -w^{3} + 4w + 1]$ $-\frac{3}{2}e^{3} + \frac{5}{2}e^{2} + 6e$
37 $[37, 37, -w^{3} + w^{2} + 2w + 1]$ $\phantom{-}e^{3} - e^{2} - 6e + 2$
49 $[49, 7, -w^{3} + 3w^{2} + 2w - 4]$ $-4e + 6$
61 $[61, 61, -w^{3} + 2w^{2} + 4w - 2]$ $\phantom{-}2e^{3} - 6e^{2} - 8e + 10$
61 $[61, 61, -w^{3} + 3w^{2} + 2w - 7]$ $\phantom{-}\frac{5}{2}e^{3} - \frac{15}{2}e^{2} - 6e + 10$
67 $[67, 67, w^{2} - 3w - 2]$ $-e^{3} + 2e^{2} + 8e - 4$
71 $[71, 71, -w^{2} + 5]$ $-e^{3} + 5e^{2} - 4e - 12$
71 $[71, 71, 2w^{3} - w^{2} - 9w - 2]$ $\phantom{-}\frac{3}{2}e^{3} - \frac{13}{2}e^{2} + 2e + 18$
71 $[71, 71, w^{2} - 2w - 5]$ $-2e^{3} + 3e^{2} + 8e$
79 $[79, 79, w^{2} - 3w - 1]$ $\phantom{-}\frac{5}{2}e^{3} - \frac{11}{2}e^{2} - 8e$
79 $[79, 79, w^{3} - 6w - 1]$ $\phantom{-}e^{2} - 4e - 8$
89 $[89, 89, -w^{3} + 3w^{2} + 3w - 7]$ $\phantom{-}e^{3} - e^{2} - 7e - 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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