Properties

Label 3.3.993.1-15.1-g
Base field 3.3.993.1
Weight $[2, 2, 2]$
Level norm $15$
Level $[15, 15, w + 3]$
Dimension $2$
CM no
Base change no

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Base field 3.3.993.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 3\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[15, 15, w + 3]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $11$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w]$ $\phantom{-}1$
3 $[3, 3, w - 1]$ $\phantom{-}e$
5 $[5, 5, -w + 2]$ $\phantom{-}1$
7 $[7, 7, w + 1]$ $-e - 2$
8 $[8, 2, 2]$ $\phantom{-}e - 3$
13 $[13, 13, w^{2} - w - 4]$ $-2e - 4$
17 $[17, 17, -w^{2} + 2w + 1]$ $-e$
25 $[25, 5, -w^{2} - w + 4]$ $\phantom{-}0$
31 $[31, 31, w^{2} - w - 1]$ $-2e - 4$
31 $[31, 31, 2w^{2} - w - 14]$ $\phantom{-}6e + 2$
31 $[31, 31, w^{2} - 2]$ $\phantom{-}2e + 4$
37 $[37, 37, -3w^{2} + w + 19]$ $\phantom{-}3e + 6$
49 $[49, 7, w^{2} - 2w - 4]$ $-6e$
53 $[53, 53, -w - 4]$ $-8e - 2$
61 $[61, 61, 2w^{2} + w - 7]$ $-2e - 8$
71 $[71, 71, 2w^{2} - 2w - 13]$ $\phantom{-}2e - 10$
73 $[73, 73, w - 5]$ $-12$
83 $[83, 83, w^{2} - 3w - 2]$ $-2e$
89 $[89, 89, w^{2} + 2w - 4]$ $-4e - 6$
97 $[97, 97, -w^{2} + 2w + 7]$ $\phantom{-}5e - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w]$ $-1$
$5$ $[5, 5, -w + 2]$ $-1$