Properties

Base field \(\Q(\sqrt{157}) \)
Weight [2, 2]
Level norm 9
Level $[9, 3, 3]$
Label 2.2.157.1-9.1-e
Dimension 6
CM no
Base change yes

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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 $[9, 3, 3]$
Label 2.2.157.1-9.1-e
Dimension 6
Is CM no
Is base change yes
Parent newspace dimension 19

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut 9x^{5} \) \(\mathstrut +\mathstrut 17x^{4} \) \(\mathstrut +\mathstrut 46x^{3} \) \(\mathstrut -\mathstrut 153x^{2} \) \(\mathstrut +\mathstrut 61x \) \(\mathstrut +\mathstrut 29\)

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Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $-1$
3 $[3, 3, -w + 7]$ $-1$
4 $[4, 2, 2]$ $\phantom{-}e$
11 $[11, 11, -3w - 17]$ $-e^{5} + 5e^{4} + 3e^{3} - 33e^{2} + 16e + 4$
11 $[11, 11, 3w - 20]$ $-e^{5} + 5e^{4} + 3e^{3} - 33e^{2} + 16e + 4$
13 $[13, 13, 2w - 13]$ $-\frac{1}{2}e^{5} + 3e^{4} - \frac{1}{2}e^{3} - \frac{39}{2}e^{2} + 21e + \frac{3}{2}$
13 $[13, 13, 2w + 11]$ $-\frac{1}{2}e^{5} + 3e^{4} - \frac{1}{2}e^{3} - \frac{39}{2}e^{2} + 21e + \frac{3}{2}$
17 $[17, 17, w + 7]$ $-\frac{3}{2}e^{5} + 8e^{4} + \frac{7}{2}e^{3} - \frac{111}{2}e^{2} + 32e + \frac{29}{2}$
17 $[17, 17, -w + 8]$ $-\frac{3}{2}e^{5} + 8e^{4} + \frac{7}{2}e^{3} - \frac{111}{2}e^{2} + 32e + \frac{29}{2}$
19 $[19, 19, -w - 4]$ $\phantom{-}e^{5} - 5e^{4} - 4e^{3} + 35e^{2} - 9e - 8$
19 $[19, 19, -w + 5]$ $\phantom{-}e^{5} - 5e^{4} - 4e^{3} + 35e^{2} - 9e - 8$
25 $[25, 5, 5]$ $-e^{5} + 5e^{4} + 3e^{3} - 34e^{2} + 18e + 15$
31 $[31, 31, -6w - 35]$ $\phantom{-}2e^{5} - 10e^{4} - 7e^{3} + 70e^{2} - 29e - 22$
31 $[31, 31, -6w + 41]$ $\phantom{-}2e^{5} - 10e^{4} - 7e^{3} + 70e^{2} - 29e - 22$
37 $[37, 37, -w - 1]$ $-\frac{5}{2}e^{5} + 13e^{4} + \frac{13}{2}e^{3} - \frac{175}{2}e^{2} + 46e + \frac{27}{2}$
37 $[37, 37, w - 2]$ $-\frac{5}{2}e^{5} + 13e^{4} + \frac{13}{2}e^{3} - \frac{175}{2}e^{2} + 46e + \frac{27}{2}$
47 $[47, 47, 3w + 16]$ $\phantom{-}e^{5} - 5e^{4} - 2e^{3} + 32e^{2} - 27e + 1$
47 $[47, 47, -3w + 19]$ $\phantom{-}e^{5} - 5e^{4} - 2e^{3} + 32e^{2} - 27e + 1$
49 $[49, 7, -7]$ $\phantom{-}\frac{3}{2}e^{5} - 8e^{4} - \frac{7}{2}e^{3} + \frac{111}{2}e^{2} - 32e - \frac{13}{2}$
67 $[67, 67, 3w - 22]$ $\phantom{-}2e^{5} - 11e^{4} - 4e^{3} + 76e^{2} - 42e - 21$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $1$
3 $[3, 3, -w + 7]$ $1$