Properties

Base field 4.4.18688.1
Weight [2, 2, 2, 2]
Level norm 14
Level $[14,14,\frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + \frac{2}{3}]$
Label 4.4.18688.1-14.2-a
Dimension 2
CM no
Base change no

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Base field 4.4.18688.1

Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} - 4x + 14\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[14,14,\frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + \frac{2}{3}]$
Label 4.4.18688.1-14.2-a
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:
\(x^{2} \) \(\mathstrut -\mathstrut 2x \) \(\mathstrut -\mathstrut 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $-1$
7 $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ $\phantom{-}e$
7 $[7, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ $\phantom{-}1$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ $\phantom{-}e - 2$
9 $[9, 3, w + 1]$ $-\frac{1}{2}e - 1$
17 $[17, 17, w + 3]$ $-\frac{3}{2}e + 2$
17 $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ $-e - 2$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ $-\frac{7}{2}e + 5$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{1}{3}]$ $\phantom{-}e$
41 $[41, 41, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 4w - \frac{19}{3}]$ $\phantom{-}e - 4$
41 $[41, 41, w^{2} - 5]$ $\phantom{-}e - 6$
41 $[41, 41, 2w + 3]$ $\phantom{-}2e + 4$
41 $[41, 41, \frac{2}{3}w^{3} + \frac{4}{3}w^{2} - 5w - \frac{29}{3}]$ $\phantom{-}\frac{5}{2}e - 8$
47 $[47, 47, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 3w - \frac{19}{3}]$ $-e + 4$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - \frac{13}{3}]$ $-\frac{1}{2}e - 8$
49 $[49, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - \frac{11}{3}]$ $-\frac{1}{2}e + 3$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 5w + \frac{19}{3}]$ $\phantom{-}\frac{3}{2}e - 3$
73 $[73, 73, -\frac{2}{3}w^{3} - \frac{1}{3}w^{2} + 4w + \frac{11}{3}]$ $-4e + 8$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + 2w - \frac{17}{3}]$ $-\frac{1}{2}e - 11$
103 $[103, 103, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + w - \frac{23}{3}]$ $-3e + 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,-\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{8}{3}]$ $1$
7 $[7,7,-\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ $-1$