Properties

Label 2.2.133.1-21.1-f
Base field \(\Q(\sqrt{133}) \)
Weight $[2, 2]$
Level norm $21$
Level $[21, 21, w + 3]$
Dimension $3$
CM no
Base change no

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Base field \(\Q(\sqrt{133}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 33\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[21, 21, w + 3]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $34$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} + x^{2} - 7x - 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 6]$ $\phantom{-}1$
3 $[3, 3, -w - 5]$ $-2$
4 $[4, 2, 2]$ $\phantom{-}e$
7 $[7, 7, 3w - 19]$ $-1$
11 $[11, 11, -2w - 11]$ $-e^{2} + 3$
11 $[11, 11, -2w + 13]$ $-2e^{2} + 2e + 12$
13 $[13, 13, w + 4]$ $\phantom{-}2e^{2} - 2e - 12$
13 $[13, 13, -w + 5]$ $\phantom{-}e^{2} - e - 6$
19 $[19, 19, 5w - 31]$ $\phantom{-}2e^{2} - 3e - 11$
23 $[23, 23, -w - 7]$ $-e^{2} + 2e + 3$
23 $[23, 23, w - 8]$ $-e^{2} + 2e + 9$
25 $[25, 5, -5]$ $-e^{2} + 9$
31 $[31, 31, -w - 1]$ $-5e^{2} + 3e + 24$
31 $[31, 31, w - 2]$ $\phantom{-}e^{2} - 3e - 6$
41 $[41, 41, 6w + 31]$ $\phantom{-}2e - 6$
41 $[41, 41, 6w - 37]$ $\phantom{-}4e^{2} - e - 21$
43 $[43, 43, -3w - 17]$ $-e^{2} + 3$
43 $[43, 43, -3w + 20]$ $\phantom{-}2e^{2} - 2e - 12$
59 $[59, 59, 3w - 17]$ $\phantom{-}e^{2} + e$
59 $[59, 59, 3w + 14]$ $-3e - 3$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w + 6]$ $-1$
$7$ $[7, 7, 3w - 19]$ $1$