Properties

Label 3.3.1425.1-15.2-d
Base field 3.3.1425.1
Weight $[2, 2, 2]$
Level norm $15$
Level $[15, 15, -w + 2]$
Dimension $2$
CM no
Base change no

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Base field 3.3.1425.1

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

Form

Weight: $[2, 2, 2]$
Level: $[15, 15, -w + 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $19$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + 2x - 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}1$
3 $[3, 3, w + 1]$ $-1$
5 $[5, 5, w^{2} - w - 7]$ $-1$
8 $[8, 2, 2]$ $\phantom{-}e$
11 $[11, 11, w - 1]$ $-e - 2$
13 $[13, 13, w^{2} - 2w - 8]$ $-e - 4$
17 $[17, 17, w^{2} - 2w - 7]$ $-4$
19 $[19, 19, -w^{2} + 2w + 4]$ $\phantom{-}1$
19 $[19, 19, -2w^{2} + 3w + 16]$ $\phantom{-}6$
23 $[23, 23, -w^{2} + 2w + 2]$ $\phantom{-}2$
31 $[31, 31, 2w^{2} - 3w - 13]$ $\phantom{-}2e + 2$
37 $[37, 37, w^{2} - w - 10]$ $-2$
43 $[43, 43, 3w^{2} - 5w - 19]$ $-2e + 4$
43 $[43, 43, w^{2} - w - 4]$ $\phantom{-}3e + 6$
43 $[43, 43, 2w^{2} - 2w - 17]$ $\phantom{-}2e + 4$
47 $[47, 47, w^{2} - 2]$ $-2e - 2$
67 $[67, 67, w^{2} - 3w - 5]$ $-8$
79 $[79, 79, -w^{2} + 3w - 1]$ $\phantom{-}e + 8$
83 $[83, 83, w^{2} + w - 4]$ $-2e - 12$
97 $[97, 97, w^{2} - 11]$ $\phantom{-}3$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 1]$ $1$
$5$ $[5, 5, w^{2} - w - 7]$ $1$