Properties

Label 2.2.101.1-5.1-b
Base field \(\Q(\sqrt{101}) \)
Weight $[2, 2]$
Level norm $5$
Level $[5, 5, -w + 5]$
Dimension $3$
CM no
Base change no

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Base field \(\Q(\sqrt{101}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 25\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[5, 5, -w + 5]$
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:

\(x^{3} + 3x^{2} - x - 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}e$
5 $[5, 5, -w + 5]$ $-1$
5 $[5, 5, -w - 4]$ $-2e^{2} - 2e + 5$
9 $[9, 3, 3]$ $-e^{2} - 2e + 1$
13 $[13, 13, w + 3]$ $\phantom{-}e^{2} + 2e - 5$
13 $[13, 13, w - 4]$ $-e^{2} + 6$
17 $[17, 17, w + 6]$ $\phantom{-}2e + 4$
17 $[17, 17, -w + 7]$ $\phantom{-}3e^{2} + 2e - 9$
19 $[19, 19, w + 2]$ $-4e^{2} - 5e + 8$
19 $[19, 19, w - 3]$ $-e^{2} + 7$
23 $[23, 23, w + 1]$ $\phantom{-}2e + 4$
23 $[23, 23, -w + 2]$ $-3e^{2} - 3e + 5$
31 $[31, 31, -w - 7]$ $-2e^{2} - 3e + 10$
31 $[31, 31, w - 8]$ $-e^{2} + e + 1$
37 $[37, 37, 2w - 9]$ $\phantom{-}2e^{2} + 4e + 3$
37 $[37, 37, 2w + 7]$ $\phantom{-}4e^{2} + 6e - 8$
43 $[43, 43, 4w + 17]$ $-e^{2} - 2e + 5$
43 $[43, 43, 4w - 21]$ $-e^{2} - 2e + 5$
47 $[47, 47, -w - 8]$ $\phantom{-}6e^{2} + 9e - 8$
47 $[47, 47, w - 9]$ $\phantom{-}4e + 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -w + 5]$ $1$