Properties

Base field \(\Q(\sqrt{157}) \)
Weight [2, 2]
Level norm 9
Level $[9,9,w + 5]$
Label 2.2.157.1-9.3-d
Dimension 5
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-d
Dimension 5
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:
\(x^{5} \) \(\mathstrut +\mathstrut x^{4} \) \(\mathstrut -\mathstrut 9x^{3} \) \(\mathstrut -\mathstrut x^{2} \) \(\mathstrut +\mathstrut 12x \) \(\mathstrut -\mathstrut 5\)

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Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $\phantom{-}e$
3 $[3, 3, -w + 7]$ $\phantom{-}0$
4 $[4, 2, 2]$ $-\frac{5}{3}e^{4} - 3e^{3} + 13e^{2} + \frac{35}{3}e - \frac{41}{3}$
11 $[11, 11, -3w - 17]$ $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 8e + 6$
11 $[11, 11, 3w - 20]$ $-e^{4} - 2e^{3} + 7e^{2} + 8e - 6$
13 $[13, 13, 2w - 13]$ $\phantom{-}e^{4} + 2e^{3} - 8e^{2} - 9e + 9$
13 $[13, 13, 2w + 11]$ $\phantom{-}e^{4} + 2e^{3} - 8e^{2} - 9e + 9$
17 $[17, 17, w + 7]$ $\phantom{-}3e^{4} + 5e^{3} - 23e^{2} - 18e + 22$
17 $[17, 17, -w + 8]$ $-3e^{4} - 5e^{3} + 23e^{2} + 18e - 22$
19 $[19, 19, -w - 4]$ $-\frac{1}{3}e^{4} + 4e^{2} - \frac{5}{3}e - \frac{19}{3}$
19 $[19, 19, -w + 5]$ $-\frac{1}{3}e^{4} + 4e^{2} - \frac{5}{3}e - \frac{19}{3}$
25 $[25, 5, 5]$ $\phantom{-}\frac{8}{3}e^{4} + 4e^{3} - 21e^{2} - \frac{41}{3}e + \frac{41}{3}$
31 $[31, 31, -6w - 35]$ $\phantom{-}\frac{7}{3}e^{4} + 3e^{3} - 20e^{2} - \frac{25}{3}e + \frac{58}{3}$
31 $[31, 31, -6w + 41]$ $\phantom{-}\frac{7}{3}e^{4} + 3e^{3} - 20e^{2} - \frac{25}{3}e + \frac{58}{3}$
37 $[37, 37, -w - 1]$ $\phantom{-}\frac{1}{3}e^{4} - 4e^{2} - \frac{4}{3}e + \frac{10}{3}$
37 $[37, 37, w - 2]$ $\phantom{-}\frac{1}{3}e^{4} - 4e^{2} - \frac{4}{3}e + \frac{10}{3}$
47 $[47, 47, 3w + 16]$ $\phantom{-}4e^{4} + 7e^{3} - 31e^{2} - 24e + 28$
47 $[47, 47, -3w + 19]$ $-4e^{4} - 7e^{3} + 31e^{2} + 24e - 28$
49 $[49, 7, -7]$ $-3e^{4} - 5e^{3} + 24e^{2} + 21e - 18$
67 $[67, 67, 3w - 22]$ $\phantom{-}3e^{4} + 6e^{3} - 22e^{2} - 26e + 17$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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