Properties

Label 2.2.357.1-9.1-g
Base field \(\Q(\sqrt{357}) \)
Weight $[2, 2]$
Level norm $9$
Level $[9, 3, 3]$
Dimension $4$
CM no
Base change no

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Base field \(\Q(\sqrt{357}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 89\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[9, 3, 3]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $114$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 4096\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}0$
4 $[4, 2, 2]$ $\phantom{-}3$
7 $[7, 7, w + 3]$ $\phantom{-}0$
11 $[11, 11, w + 3]$ $\phantom{-}\frac{1}{128}e^{3} + \frac{1}{2}e$
11 $[11, 11, w + 7]$ $-\frac{1}{128}e^{3} - \frac{1}{2}e$
17 $[17, 17, w + 8]$ $-\frac{1}{128}e^{3} + \frac{1}{2}e$
23 $[23, 23, w + 4]$ $-\frac{1}{128}e^{3} - \frac{1}{2}e$
23 $[23, 23, w + 18]$ $\phantom{-}\frac{1}{128}e^{3} + \frac{1}{2}e$
25 $[25, 5, 5]$ $\phantom{-}6$
29 $[29, 29, w + 1]$ $-\frac{1}{128}e^{3} - \frac{1}{2}e$
29 $[29, 29, w + 27]$ $\phantom{-}\frac{1}{128}e^{3} + \frac{1}{2}e$
31 $[31, 31, w + 13]$ $\phantom{-}0$
31 $[31, 31, w + 17]$ $\phantom{-}0$
43 $[43, 43, -w - 11]$ $\phantom{-}4$
43 $[43, 43, w - 12]$ $\phantom{-}4$
47 $[47, 47, -w - 6]$ $\phantom{-}\frac{1}{64}e^{3} - e$
47 $[47, 47, w - 7]$ $\phantom{-}\frac{1}{64}e^{3} - e$
59 $[59, 59, -w - 5]$ $-\frac{1}{64}e^{3} + e$
59 $[59, 59, w - 6]$ $-\frac{1}{64}e^{3} + e$
61 $[61, 61, w + 16]$ $-\frac{3}{32}e^{2}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 1]$ $1$