Properties

Label 4.4.11661.1-25.1-d
Base field 4.4.11661.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, w^{3} - 2w^{2} - 2w + 2]$
Dimension $16$
CM no
Base change no

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Base field 4.4.11661.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[25, 5, w^{3} - 2w^{2} - 2w + 2]$
Dimension: $16$
CM: no
Base change: no
Newspace dimension: $34$

Hecke eigenvalues ($q$-expansion)

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

\(x^{16} + 6x^{15} - 12x^{14} - 128x^{13} - 31x^{12} + 1031x^{11} + 1051x^{10} - 3828x^{9} - 5696x^{8} + 6123x^{7} + 12576x^{6} - 1815x^{5} - 10952x^{4} - 3792x^{3} + 1950x^{2} + 1362x + 213\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $...$
3 $[3, 3, w - 2]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $...$
16 $[16, 2, 2]$ $...$
23 $[23, 23, -w^{3} + 4w + 1]$ $...$
25 $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}1$
25 $[25, 5, w^{3} - w^{2} - 3w + 1]$ $...$
29 $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ $...$
29 $[29, 29, w^{3} - w^{2} - 5w + 1]$ $...$
43 $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ $...$
43 $[43, 43, w^{3} - w^{2} - 4w + 2]$ $...$
61 $[61, 61, -w^{2} + 2w + 4]$ $...$
61 $[61, 61, w^{2} - 5]$ $...$
79 $[79, 79, 3w^{3} - 7w^{2} - 8w + 16]$ $...$
79 $[79, 79, -w^{3} + w^{2} + 6w - 4]$ $...$
101 $[101, 101, -w^{3} + 3w^{2} + w - 7]$ $...$
101 $[101, 101, w^{3} - 4w - 4]$ $...$
103 $[103, 103, 2w^{3} - w^{2} - 8w - 1]$ $...$
103 $[103, 103, 2w^{3} - 5w^{2} - 4w + 8]$ $...$
107 $[107, 107, 2w^{2} - 3w - 4]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$25$ $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ $-1$