Properties

Base field \(\Q(\sqrt{157}) \)
Weight [2, 2]
Level norm 9
Level $[9,9,w + 5]$
Label 2.2.157.1-9.3-e
Dimension 6
CM no
Base change no

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Base field \(\Q(\sqrt{157}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 39\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[9,9,w + 5]$
Label 2.2.157.1-9.3-e
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 16

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut 11x^{4} \) \(\mathstrut +\mathstrut 28x^{2} \) \(\mathstrut -\mathstrut 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{11}{4}e^{2} + 5$
3 $[3, 3, -w + 7]$ $\phantom{-}0$
4 $[4, 2, 2]$ $\phantom{-}e$
11 $[11, 11, -3w - 17]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{11}{4}e^{3} + 7e$
11 $[11, 11, 3w - 20]$ $\phantom{-}\frac{3}{4}e^{4} - \frac{25}{4}e^{2} + 7$
13 $[13, 13, 2w - 13]$ $\phantom{-}\frac{5}{4}e^{4} - \frac{43}{4}e^{2} + 13$
13 $[13, 13, 2w + 11]$ $-\frac{1}{4}e^{4} + \frac{11}{4}e^{2} - 2$
17 $[17, 17, w + 7]$ $-\frac{1}{4}e^{5} + \frac{11}{4}e^{3} - 6e$
17 $[17, 17, -w + 8]$ $-\frac{1}{4}e^{4} + \frac{11}{4}e^{2} - 4$
19 $[19, 19, -w - 4]$ $-\frac{3}{4}e^{5} + \frac{29}{4}e^{3} - 10e$
19 $[19, 19, -w + 5]$ $-e^{3} + 5e$
25 $[25, 5, 5]$ $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 7e$
31 $[31, 31, -6w - 35]$ $-\frac{1}{2}e^{5} + \frac{7}{2}e^{3}$
31 $[31, 31, -6w + 41]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{7}{4}e^{3}$
37 $[37, 37, -w - 1]$ $\phantom{-}\frac{3}{4}e^{5} - \frac{29}{4}e^{3} + 13e$
37 $[37, 37, w - 2]$ $\phantom{-}e^{3} - 8e$
47 $[47, 47, 3w + 16]$ $\phantom{-}\frac{3}{4}e^{4} - \frac{21}{4}e^{2} + 8$
47 $[47, 47, -3w + 19]$ $-\frac{3}{2}e^{5} + \frac{29}{2}e^{3} - 22e$
49 $[49, 7, -7]$ $-\frac{1}{4}e^{4} + \frac{3}{4}e^{2} + 2$
67 $[67, 67, 3w - 22]$ $\phantom{-}e^{4} - 9e^{2} + 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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