Properties

Label 3.3.1825.1-5.1-b
Base field 3.3.1825.1
Weight $[2, 2, 2]$
Level norm $5$
Level $[5, 5, -w + 2]$
Dimension $4$
CM no
Base change no

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Base field 3.3.1825.1

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

Form

Weight: $[2, 2, 2]$
Level: $[5, 5, -w + 2]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 5x^{2} + 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w + 2]$ $-1$
7 $[7, 7, w]$ $\phantom{-}e$
8 $[8, 2, 2]$ $\phantom{-}e^{2} - 3$
11 $[11, 11, w + 2]$ $-e^{3} + 4e$
13 $[13, 13, w + 1]$ $\phantom{-}e^{3} - 5e$
17 $[17, 17, -w^{2} - w + 4]$ $-2e$
23 $[23, 23, -w^{2} + 6]$ $\phantom{-}2e^{3} - 6e$
23 $[23, 23, -w^{2} - w + 3]$ $-3e^{3} + 12e$
23 $[23, 23, -w + 4]$ $-e^{2} + 3$
27 $[27, 3, 3]$ $-3e^{2} + 4$
29 $[29, 29, -w^{2} - 2w + 4]$ $-3e^{2} + 3$
31 $[31, 31, w^{2} - 10]$ $-5$
41 $[41, 41, w + 4]$ $\phantom{-}3e^{2} - 12$
41 $[41, 41, w^{2} - 5]$ $\phantom{-}4e^{3} - 16e$
41 $[41, 41, -2w - 5]$ $-5e$
43 $[43, 43, w^{2} - w - 4]$ $-3e^{3} + 12e$
47 $[47, 47, w^{2} - w - 9]$ $\phantom{-}e^{3} - 3e$
49 $[49, 7, w^{2} - w - 8]$ $\phantom{-}4e^{3} - 12e$
53 $[53, 53, 2w^{2} + w - 12]$ $-5e$
59 $[59, 59, w^{2} - 3]$ $-2e^{3} + 10e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -w + 2]$ $1$