Properties

Label 2.2.29.1-13.1-b
Base field \(\Q(\sqrt{29}) \)
Weight $[2, 2]$
Level norm $13$
Level $[13, 13, w + 4]$
Dimension $3$
CM no
Base change no

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Base field \(\Q(\sqrt{29}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 7\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[13, 13, w + 4]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - x^{2} - 12x + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}e$
5 $[5, 5, w + 1]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 4$
5 $[5, 5, w - 2]$ $-\frac{1}{4}e^{2} + \frac{1}{4}e + 4$
7 $[7, 7, w]$ $-\frac{1}{2}e^{2} - \frac{1}{2}e + 2$
7 $[7, 7, -w + 1]$ $\phantom{-}\frac{3}{4}e^{2} + \frac{1}{4}e - 5$
9 $[9, 3, 3]$ $-\frac{3}{4}e^{2} - \frac{5}{4}e + 7$
13 $[13, 13, w + 4]$ $-1$
13 $[13, 13, w - 5]$ $-\frac{3}{4}e^{2} - \frac{1}{4}e + 6$
23 $[23, 23, -w - 5]$ $\phantom{-}e^{2} - 8$
23 $[23, 23, w - 6]$ $\phantom{-}\frac{1}{4}e^{2} + \frac{3}{4}e$
29 $[29, 29, 2w - 1]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 6$
53 $[53, 53, 3w - 5]$ $-\frac{1}{2}e^{2} - \frac{5}{2}e + 2$
53 $[53, 53, -3w - 2]$ $-2e^{2} - e + 18$
59 $[59, 59, -3w - 1]$ $\phantom{-}\frac{1}{4}e^{2} - \frac{1}{4}e - 1$
59 $[59, 59, 3w - 4]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{5}{2}e - 10$
67 $[67, 67, 3w - 13]$ $\phantom{-}\frac{3}{4}e^{2} + \frac{13}{4}e - 9$
67 $[67, 67, -3w - 10]$ $-\frac{1}{2}e^{2} + \frac{3}{2}e + 10$
71 $[71, 71, 2w - 11]$ $\phantom{-}e^{2} + 2e - 12$
71 $[71, 71, -2w - 9]$ $-\frac{3}{4}e^{2} - \frac{5}{4}e + 6$
83 $[83, 83, -w - 9]$ $-\frac{1}{2}e^{2} - \frac{3}{2}e + 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, w + 4]$ $1$