Properties

Label 4.4.16357.1-15.1-b
Base field 4.4.16357.1
Weight $[2, 2, 2, 2]$
Level norm $15$
Level $[15, 15, -w^{3} + 5w + 1]$
Dimension $3$
CM no
Base change no

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Base field 4.4.16357.1

Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[15, 15, -w^{3} + 5w + 1]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} + 2x^{2} - 8x - 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $-1$
5 $[5, 5, -w^{3} + 5w + 2]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $\phantom{-}1$
11 $[11, 11, -w^{3} + 5w]$ $\phantom{-}\frac{1}{2}e^{2} - 4$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $\phantom{-}\frac{1}{2}e^{2} + e$
16 $[16, 2, 2]$ $-\frac{1}{2}e^{2} - e + 3$
19 $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ $-e^{2} - 2e + 4$
25 $[25, 5, -w^{2} + w + 3]$ $-e^{2} - e + 4$
27 $[27, 3, w^{3} - w^{2} - 5w + 4]$ $\phantom{-}\frac{1}{2}e^{2} + 2e - 8$
31 $[31, 31, -w - 3]$ $\phantom{-}e^{2} - 4$
37 $[37, 37, -w^{3} - w^{2} + 6w + 4]$ $-3e - 4$
41 $[41, 41, w^{3} + w^{2} - 6w - 5]$ $-\frac{1}{2}e^{2} - e - 4$
43 $[43, 43, w^{3} - 7w - 2]$ $\phantom{-}2e + 4$
47 $[47, 47, -2w^{3} + 11w + 2]$ $-2e - 8$
61 $[61, 61, w^{2} - 3]$ $\phantom{-}e^{2} - 3e - 12$
67 $[67, 67, w^{2} + w - 4]$ $-e^{2}$
79 $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ $\phantom{-}\frac{1}{2}e^{2} + 2e - 8$
97 $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ $-e^{2} - 4e + 6$
97 $[97, 97, -w^{3} + 6w - 3]$ $-2e^{2} - 2e + 2$
97 $[97, 97, -3w^{3} + 16w]$ $-e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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