Properties

Base field \(\Q(\sqrt{197}) \)
Weight [2, 2]
Level norm 23
Level $[23, 23, w + 8]$
Label 2.2.197.1-23.1-b
Dimension 3
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 $[23, 23, w + 8]$
Label 2.2.197.1-23.1-b
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 81

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} \) \(\mathstrut -\mathstrut x^{2} \) \(\mathstrut -\mathstrut 6x \) \(\mathstrut +\mathstrut 4\)

  Show full eigenvalues   Hide large eigenvalues

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
23 $[23, 23, w + 8]$ $-1$