Properties

Label 4.4.2225.1-29.2-a
Base field 4.4.2225.1
Weight $[2, 2, 2, 2]$
Level norm $29$
Level $[29,29,-w^{2} + 5]$
Dimension $1$
CM no
Base change no

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Base field 4.4.2225.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[29,29,-w^{2} + 5]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $1$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -w]$ $\phantom{-}3$
4 $[4, 2, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 1]$ $\phantom{-}1$
19 $[19, 19, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + 4]$ $\phantom{-}0$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - 1]$ $\phantom{-}0$
25 $[25, 5, w^{3} - w^{2} - 3w + 1]$ $-2$
29 $[29, 29, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{3}{2}w - 1]$ $-6$
29 $[29, 29, -w^{2} + 5]$ $-1$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 3]$ $-4$
31 $[31, 31, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ $\phantom{-}0$
41 $[41, 41, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{5}{2}w]$ $-10$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{1}{2}w - 5]$ $\phantom{-}2$
59 $[59, 59, w^{3} - w^{2} - 5w + 1]$ $\phantom{-}0$
59 $[59, 59, \frac{3}{2}w^{3} - \frac{1}{2}w^{2} - \frac{11}{2}w - 1]$ $\phantom{-}4$
61 $[61, 61, \frac{3}{2}w^{3} - \frac{1}{2}w^{2} - \frac{11}{2}w - 2]$ $\phantom{-}2$
61 $[61, 61, -2w^{2} + w + 7]$ $\phantom{-}2$
71 $[71, 71, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{5}{2}w + 6]$ $\phantom{-}8$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} - \frac{1}{2}w - 5]$ $\phantom{-}0$
71 $[71, 71, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 5]$ $\phantom{-}8$
71 $[71, 71, -w^{3} + 3w^{2} + 2w - 7]$ $\phantom{-}4$
81 $[81, 3, -3]$ $-10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29,29,-w^{2} + 5]$ $1$