Properties

Base field 4.4.18432.1
Weight [2, 2, 2, 2]
Level norm 14
Level $[14, 14, w + 2]$
Label 4.4.18432.1-14.1-d
Dimension 2
CM no
Base change no

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Base field 4.4.18432.1

Generator \(w\), with minimal polynomial \(x^{4} - 12x^{2} + 18\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[14, 14, w + 2]$
Label 4.4.18432.1-14.1-d
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 18

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} \) \(\mathstrut +\mathstrut 2x \) \(\mathstrut -\mathstrut 7\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ $\phantom{-}1$
7 $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ $-\frac{1}{2}e - \frac{5}{2}$
7 $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ $-1$
7 $[7, 7, \frac{1}{3}w^{2} + w - 1]$ $-\frac{1}{2}e - \frac{1}{2}$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ $\phantom{-}e$
9 $[9, 3, w - 3]$ $\phantom{-}\frac{1}{2}e + \frac{1}{2}$
41 $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $-e + 3$
41 $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ $-2e - 6$
41 $[41, 41, \frac{1}{3}w^{2} + w - 3]$ $-\frac{3}{2}e - \frac{5}{2}$
41 $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ $\phantom{-}\frac{5}{2}e + \frac{13}{2}$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ $-\frac{1}{2}e - \frac{17}{2}$
47 $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ $-3e + 1$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $\phantom{-}\frac{3}{2}e + \frac{1}{2}$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $\phantom{-}e + 4$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ $\phantom{-}3e - 6$
89 $[89, 89, \frac{2}{3}w^{2} + w - 5]$ $-3e + 3$
89 $[89, 89, \frac{2}{3}w^{2} - w - 5]$ $-\frac{3}{2}e - \frac{29}{2}$
89 $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ $\phantom{-}\frac{3}{2}e + \frac{7}{2}$
97 $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ $\phantom{-}\frac{1}{2}e - \frac{27}{2}$
97 $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ $\phantom{-}\frac{3}{2}e - \frac{17}{2}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ $-1$
7 $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ $1$