Properties

Label 3.3.1492.1-14.1-j
Base field 3.3.1492.1
Weight $[2, 2, 2]$
Level norm $14$
Level $[14, 14, -w^{2} + 3w + 4]$
Dimension $2$
CM no
Base change no

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Base field 3.3.1492.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 5\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[14, 14, -w^{2} + 3w + 4]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 18\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 1]$ $-1$
5 $[5, 5, w]$ $\phantom{-}0$
7 $[7, 7, w^{2} - 2w - 8]$ $\phantom{-}1$
7 $[7, 7, -2w^{2} + 3w + 16]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 2w + 6]$ $\phantom{-}\frac{1}{3}e$
11 $[11, 11, w^{2} - 2w - 2]$ $\phantom{-}0$
19 $[19, 19, -w + 2]$ $\phantom{-}e$
23 $[23, 23, -w^{2} + 3w + 1]$ $-8$
25 $[25, 5, w^{2} - w - 9]$ $-\frac{1}{3}e$
27 $[27, 3, 3]$ $-2$
29 $[29, 29, -w^{2} - w + 1]$ $-\frac{5}{3}e$
29 $[29, 29, w^{2} - 2w - 4]$ $\phantom{-}\frac{2}{3}e$
29 $[29, 29, -w^{2} + w + 11]$ $\phantom{-}8$
43 $[43, 43, 2w^{2} - 3w - 18]$ $\phantom{-}8$
47 $[47, 47, -2w + 7]$ $\phantom{-}\frac{5}{3}e$
53 $[53, 53, w^{2} - w - 3]$ $-\frac{5}{3}e$
61 $[61, 61, w^{2} + 2w + 2]$ $\phantom{-}0$
67 $[67, 67, -2w^{2} + 5w + 8]$ $\phantom{-}\frac{8}{3}e$
79 $[79, 79, w^{2} - 3w - 9]$ $\phantom{-}10$
97 $[97, 97, -w^{2} - 2w + 2]$ $\phantom{-}4e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w - 1]$ $1$
$7$ $[7, 7, w^{2} - 2w - 8]$ $-1$