Properties

Label 4.4.16357.1-15.1-c
Base field 4.4.16357.1
Weight $[2, 2, 2, 2]$
Level norm $15$
Level $[15, 15, -w^{3} + 5w + 1]$
Dimension $4$
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: $4$
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:

\(x^{4} - 6x^{3} + 6x^{2} + 12x - 12\)

  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 $[5, 5, w - 1]$ $-1$
11 $[11, 11, -w^{3} + 5w]$ $-e^{3} + 4e^{2} + e - 6$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $\phantom{-}e^{3} - 4e^{2} + 8$
16 $[16, 2, 2]$ $-\frac{1}{2}e^{3} + e^{2} + 3e + 1$
19 $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 3e + 4$
25 $[25, 5, -w^{2} + w + 3]$ $\phantom{-}\frac{1}{2}e^{3} - 2e^{2} - 2e + 8$
27 $[27, 3, w^{3} - w^{2} - 5w + 4]$ $-\frac{1}{2}e^{3} + e^{2} + 4e - 4$
31 $[31, 31, -w - 3]$ $\phantom{-}e^{3} - 5e^{2} + 2e + 10$
37 $[37, 37, -w^{3} - w^{2} + 6w + 4]$ $-\frac{1}{2}e^{3} + 2e^{2} + 2e - 4$
41 $[41, 41, w^{3} + w^{2} - 6w - 5]$ $-2e^{2} + 2e + 12$
43 $[43, 43, w^{3} - 7w - 2]$ $\phantom{-}e^{3} - 5e^{2} + 2e + 8$
47 $[47, 47, -2w^{3} + 11w + 2]$ $\phantom{-}\frac{1}{2}e^{3} - 2e^{2} + e + 6$
61 $[61, 61, w^{2} - 3]$ $\phantom{-}\frac{3}{2}e^{3} - 7e^{2} + 16$
67 $[67, 67, w^{2} + w - 4]$ $\phantom{-}e^{3} - 3e^{2} - 6e + 10$
79 $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ $-2e^{3} + 8e^{2} - 3e - 8$
97 $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ $-e^{3} + 8e^{2} - 10e - 14$
97 $[97, 97, -w^{3} + 6w - 3]$ $\phantom{-}3e^{3} - 11e^{2} + 10$
97 $[97, 97, -3w^{3} + 16w]$ $\phantom{-}e^{3} - 4e^{2} - 5e + 14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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