Properties

Base field \(\Q(\sqrt{197}) \)
Weight [2, 2]
Level norm 9
Level $[9, 3, 3]$
Label 2.2.197.1-9.1-c
Dimension 2
CM no
Base change no

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Base field \(\Q(\sqrt{197}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 49\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[9, 3, 3]$
Label 2.2.197.1-9.1-c
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 30

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} \) \(\mathstrut +\mathstrut 2x \) \(\mathstrut -\mathstrut 55\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $-2$
7 $[7, 7, w - 7]$ $\phantom{-}1$
7 $[7, 7, w + 6]$ $\phantom{-}1$
9 $[9, 3, 3]$ $\phantom{-}1$
19 $[19, 19, w + 5]$ $-e - 2$
19 $[19, 19, w - 6]$ $\phantom{-}e$
23 $[23, 23, w + 8]$ $\phantom{-}\frac{1}{2}e + \frac{7}{2}$
23 $[23, 23, -w + 9]$ $-\frac{1}{2}e + \frac{5}{2}$
25 $[25, 5, 5]$ $-2$
29 $[29, 29, -w - 4]$ $-\frac{1}{2}e - \frac{11}{2}$
29 $[29, 29, w - 5]$ $\phantom{-}\frac{1}{2}e - \frac{9}{2}$
37 $[37, 37, -w - 3]$ $-e + 2$
37 $[37, 37, w - 4]$ $\phantom{-}e + 4$
41 $[41, 41, -w - 9]$ $\phantom{-}\frac{1}{2}e - \frac{13}{2}$
41 $[41, 41, w - 10]$ $-\frac{1}{2}e - \frac{15}{2}$
43 $[43, 43, -w - 2]$ $\phantom{-}9$
43 $[43, 43, w - 3]$ $\phantom{-}9$
47 $[47, 47, -w - 1]$ $-\frac{3}{2}e - \frac{5}{2}$
47 $[47, 47, w - 2]$ $\phantom{-}\frac{3}{2}e + \frac{1}{2}$
53 $[53, 53, 2w - 13]$ $-e - 3$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, 3]$ $-1$