Properties

Label 2.2.29.1-49.2-e
Base field \(\Q(\sqrt{29}) \)
Weight $[2, 2]$
Level norm $49$
Level $[49, 49, w + 7]$
Dimension $2$
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: $[49, 49, w + 7]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $-1$
5 $[5, 5, w + 1]$ $\phantom{-}4$
5 $[5, 5, w - 2]$ $\phantom{-}e$
7 $[7, 7, w]$ $\phantom{-}0$
7 $[7, 7, -w + 1]$ $-3e$
9 $[9, 3, 3]$ $\phantom{-}2e$
13 $[13, 13, w + 4]$ $\phantom{-}6$
13 $[13, 13, w - 5]$ $-2e$
23 $[23, 23, -w - 5]$ $\phantom{-}5e$
23 $[23, 23, w - 6]$ $-2e$
29 $[29, 29, 2w - 1]$ $\phantom{-}2e$
53 $[53, 53, 3w - 5]$ $-2$
53 $[53, 53, -3w - 2]$ $-2$
59 $[59, 59, -3w - 1]$ $-8$
59 $[59, 59, 3w - 4]$ $\phantom{-}5e$
67 $[67, 67, 3w - 13]$ $-5e$
67 $[67, 67, -3w - 10]$ $\phantom{-}2e$
71 $[71, 71, 2w - 11]$ $\phantom{-}0$
71 $[71, 71, -2w - 9]$ $\phantom{-}0$
83 $[83, 83, -w - 9]$ $-6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, w]$ $1$