Properties

Label 4.4.5725.1-29.2-c
Base field 4.4.5725.1
Weight $[2, 2, 2, 2]$
Level norm $29$
Level $[29,29,-\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$
Dimension $1$
CM no
Base change no

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Base field 4.4.5725.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + 6x + 11\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[29,29,-\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
9 $[9, 3, \frac{1}{3}w^{3} - \frac{8}{3}w - \frac{2}{3}]$ $-4$
9 $[9, 3, -w + 1]$ $-1$
11 $[11, 11, w]$ $-3$
11 $[11, 11, -\frac{1}{3}w^{3} + \frac{2}{3}w + \frac{5}{3}]$ $\phantom{-}3$
11 $[11, 11, \frac{1}{3}w^{3} - \frac{8}{3}w + \frac{1}{3}]$ $\phantom{-}3$
11 $[11, 11, -\frac{2}{3}w^{3} + \frac{13}{3}w + \frac{4}{3}]$ $\phantom{-}0$
16 $[16, 2, 2]$ $-7$
25 $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ $-2$
29 $[29, 29, -w - 3]$ $-9$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ $\phantom{-}1$
31 $[31, 31, w^{3} - 6w + 1]$ $\phantom{-}4$
31 $[31, 31, w^{3} - 6w - 2]$ $\phantom{-}4$
41 $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ $\phantom{-}3$
41 $[41, 41, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{5}{3}]$ $\phantom{-}3$
59 $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ $\phantom{-}3$
59 $[59, 59, w^{3} + w^{2} - 6w - 4]$ $\phantom{-}0$
79 $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ $-11$
79 $[79, 79, \frac{1}{3}w^{3} + w^{2} - \frac{2}{3}w - \frac{17}{3}]$ $-8$
89 $[89, 89, \frac{4}{3}w^{3} - \frac{23}{3}w - \frac{5}{3}]$ $-6$
89 $[89, 89, \frac{1}{3}w^{3} + 2w^{2} - \frac{5}{3}w - \frac{32}{3}]$ $-15$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29,29,-\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ $-1$