Properties

Label 4.4.9301.1-25.1-g
Base field 4.4.9301.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 25, -w^{3} + w^{2} + 3w - 1]$
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: $[25, 25, -w^{3} + w^{2} + 3w - 1]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 7x^{2} + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
5 $[5, 5, -w^{3} + w^{2} + 4w + 1]$ $\phantom{-}0$
7 $[7, 7, -w^{2} + 2]$ $-e^{2} + 2$
7 $[7, 7, -w^{2} + w + 2]$ $\phantom{-}0$
16 $[16, 2, 2]$ $\phantom{-}\frac{3}{2}e^{3} - \frac{15}{2}e$
17 $[17, 17, -w^{3} + w^{2} + 4w - 2]$ $-e^{2} - 1$
23 $[23, 23, -w^{3} + 2w^{2} + 3w - 2]$ $-2e^{3} + 12e$
27 $[27, 3, -w^{3} + w^{2} + 5w - 1]$ $-4$
37 $[37, 37, -w^{3} + 4w + 1]$ $\phantom{-}\frac{3}{2}e^{3} - \frac{21}{2}e$
37 $[37, 37, -w^{3} + w^{2} + 2w + 1]$ $-\frac{3}{2}e^{3} + \frac{15}{2}e$
49 $[49, 7, -w^{3} + 3w^{2} + 2w - 4]$ $-1$
61 $[61, 61, -w^{3} + 2w^{2} + 4w - 2]$ $\phantom{-}e^{2} - 11$
61 $[61, 61, -w^{3} + 3w^{2} + 2w - 7]$ $-\frac{1}{2}e^{3} + \frac{11}{2}e$
67 $[67, 67, w^{2} - 3w - 2]$ $\phantom{-}3e^{3} - 21e$
71 $[71, 71, -w^{2} + 5]$ $-4e^{3} + 21e$
71 $[71, 71, 2w^{3} - w^{2} - 9w - 2]$ $\phantom{-}3e$
71 $[71, 71, w^{2} - 2w - 5]$ $\phantom{-}e^{3} - 12e$
79 $[79, 79, w^{2} - 3w - 1]$ $\phantom{-}2e^{2} - 16$
79 $[79, 79, w^{3} - 6w - 1]$ $\phantom{-}2e^{2} - 10$
89 $[89, 89, -w^{3} + 3w^{2} + 3w - 7]$ $\phantom{-}3e^{2} - 3$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -w^{3} + w^{2} + 4w + 1]$ $-1$