Properties

Label 4.4.15125.1-11.1-c
Base field 4.4.15125.1
Weight $[2, 2, 2, 2]$
Level norm $11$
Level $[11, 11, 2w^{3} + 3w^{2} - 18w - 16]$
Dimension $4$
CM no
Base change no

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Base field 4.4.15125.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 14x^{2} + 14x + 31\); narrow class number \(4\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[11, 11, 2w^{3} + 3w^{2} - 18w - 16]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 66x^{2} + 900\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, 4w^{3} + 7w^{2} - 37w - 45]$ $\phantom{-}3$
11 $[11, 11, 2w^{3} + 3w^{2} - 18w - 16]$ $-1$
11 $[11, 11, -w + 2]$ $\phantom{-}2$
16 $[16, 2, 2]$ $\phantom{-}0$
19 $[19, 19, 4w^{3} + 7w^{2} - 36w - 45]$ $\phantom{-}e$
19 $[19, 19, -w^{3} - w^{2} + 9w + 3]$ $\phantom{-}\frac{1}{30}e^{3} - \frac{11}{5}e$
19 $[19, 19, -2w^{3} - 4w^{2} + 17w + 23]$ $\phantom{-}\frac{1}{45}e^{3} - \frac{17}{15}e$
19 $[19, 19, w^{3} + 2w^{2} - 10w - 10]$ $\phantom{-}\frac{1}{90}e^{3} - \frac{1}{15}e$
29 $[29, 29, -w - 2]$ $-\frac{1}{45}e^{3} + \frac{17}{15}e$
29 $[29, 29, -w^{3} - 2w^{2} + 8w + 15]$ $-\frac{1}{90}e^{3} + \frac{1}{15}e$
29 $[29, 29, 2w^{3} + 3w^{2} - 18w - 20]$ $-\frac{1}{90}e^{3} + \frac{1}{15}e$
29 $[29, 29, -3w^{3} - 5w^{2} + 27w + 28]$ $-\frac{1}{45}e^{3} + \frac{17}{15}e$
31 $[31, 31, 3w^{3} + 5w^{2} - 27w - 31]$ $\phantom{-}\frac{1}{3}e^{2} - 9$
31 $[31, 31, -3w^{3} - 5w^{2} + 27w + 30]$ $\phantom{-}\frac{1}{3}e^{2} - 9$
31 $[31, 31, -2w^{3} - 3w^{2} + 18w + 17]$ $-\frac{1}{3}e^{2} + 13$
31 $[31, 31, 2w^{3} + 3w^{2} - 18w - 18]$ $-\frac{1}{3}e^{2} + 13$
71 $[71, 71, -w^{3} - 2w^{2} + 10w + 8]$ $-\frac{1}{3}e^{2} + 17$
71 $[71, 71, 4w^{3} + 8w^{2} - 35w - 50]$ $-\frac{2}{3}e^{2} + 21$
71 $[71, 71, -4w^{3} - 7w^{2} + 36w + 47]$ $\phantom{-}\frac{2}{3}e^{2} - 23$
71 $[71, 71, -w^{3} - 2w^{2} + 8w + 17]$ $\phantom{-}\frac{1}{3}e^{2} - 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11, 11, 2w^{3} + 3w^{2} - 18w - 16]$ $1$