Properties

Label 4.4.18736.1-15.1-l
Base field 4.4.18736.1
Weight $[2, 2, 2, 2]$
Level norm $15$
Level $[15, 15, -w^{2} + 2w + 5]$
Dimension $4$
CM no
Base change no

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Base field 4.4.18736.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 4x + 5\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[15, 15, -w^{2} + 2w + 5]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $24$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + x^{3} - 9x^{2} - 9x - 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w - 1]$ $-1$
4 $[4, 2, -w^{3} + 2w^{2} + 4w - 3]$ $\phantom{-}e$
5 $[5, 5, w]$ $-1$
7 $[7, 7, w - 2]$ $\phantom{-}2$
11 $[11, 11, w^{2} - 2w - 4]$ $-4e^{3} - 2e^{2} + 36e + 18$
23 $[23, 23, -w^{2} + 2w + 1]$ $-2e^{3} - e^{2} + 19e + 14$
23 $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ $-e^{3} + 11e + 2$
27 $[27, 3, -w^{3} + w^{2} + 6w + 2]$ $-e^{3} + 7e + 2$
31 $[31, 31, -w^{3} + 3w^{2} + w - 1]$ $\phantom{-}5e^{3} + 3e^{2} - 48e - 24$
31 $[31, 31, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}e^{3} - 7e - 2$
37 $[37, 37, w^{2} - 2w - 6]$ $-4e^{3} - 2e^{2} + 38e + 18$
37 $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ $\phantom{-}2e^{3} + 3e^{2} - 19e - 18$
43 $[43, 43, w^{2} - 3w - 2]$ $-2e^{3} - e^{2} + 17e + 2$
61 $[61, 61, -w^{3} + 2w^{2} + 2w - 2]$ $-e^{3} + 11e$
73 $[73, 73, w^{3} - 3w^{2} - 2w + 3]$ $-3e^{3} + 27e + 10$
83 $[83, 83, -w - 3]$ $-2e^{3} + 18e + 14$
89 $[89, 89, -w^{3} + 3w^{2} + 2w - 2]$ $-2e^{3} - e^{2} + 21e + 18$
89 $[89, 89, 2w - 1]$ $\phantom{-}2e^{3} - 20e$
101 $[101, 101, w^{3} - 4w^{2} + w + 7]$ $\phantom{-}8e^{3} + 4e^{2} - 74e - 34$
101 $[101, 101, 2w^{2} - 3w - 3]$ $\phantom{-}6e^{3} + 4e^{2} - 60e - 34$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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