Properties

Label 3.3.1345.1-25.3-b
Base field 3.3.1345.1
Weight $[2, 2, 2]$
Level norm $25$
Level $[25, 25, -w^{2} - w + 5]$
Dimension $2$
CM no
Base change no

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Base field 3.3.1345.1

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

Form

Weight: $[2, 2, 2]$
Level: $[25, 25, -w^{2} - w + 5]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $36$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w - 1]$ $\phantom{-}0$
5 $[5, 5, w + 2]$ $\phantom{-}e$
7 $[7, 7, w + 3]$ $-e - 1$
7 $[7, 7, -w + 2]$ $-e$
7 $[7, 7, -w + 1]$ $\phantom{-}e - 2$
8 $[8, 2, 2]$ $-1$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}0$
19 $[19, 19, -w^{2} + 5]$ $\phantom{-}2e - 2$
23 $[23, 23, -w^{2} - w + 3]$ $\phantom{-}e - 2$
27 $[27, 3, 3]$ $\phantom{-}4$
29 $[29, 29, w^{2} - w - 3]$ $-e + 1$
31 $[31, 31, w^{2} - w - 8]$ $\phantom{-}4e - 2$
37 $[37, 37, -w - 4]$ $\phantom{-}2e - 6$
43 $[43, 43, 2w^{2} - 4w - 3]$ $\phantom{-}e - 3$
47 $[47, 47, w^{2} - 3]$ $\phantom{-}3e - 1$
53 $[53, 53, 2w^{2} - w - 11]$ $\phantom{-}2$
59 $[59, 59, w^{2} - 2w - 4]$ $-2e + 2$
67 $[67, 67, w^{2} + w - 8]$ $-e + 7$
71 $[71, 71, w^{2} + w - 11]$ $-2e + 6$
73 $[73, 73, -w^{2} + 4w - 2]$ $-2e + 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -w - 1]$ $-1$