Properties

Base field \(\Q(\sqrt{157}) \)
Weight [2, 2]
Level norm 4
Level $[4, 2, 2]$
Label 2.2.157.1-4.1-c
Dimension 7
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 $[4, 2, 2]$
Label 2.2.157.1-4.1-c
Dimension 7
Is CM no
Is base change yes
Parent newspace dimension 11

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} \) \(\mathstrut -\mathstrut 3x^{6} \) \(\mathstrut -\mathstrut 9x^{5} \) \(\mathstrut +\mathstrut 26x^{4} \) \(\mathstrut +\mathstrut 16x^{3} \) \(\mathstrut -\mathstrut 37x^{2} \) \(\mathstrut -\mathstrut 5x \) \(\mathstrut +\mathstrut 2\)

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Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $\phantom{-}e$
3 $[3, 3, -w + 7]$ $\phantom{-}e$
4 $[4, 2, 2]$ $-1$
11 $[11, 11, -3w - 17]$ $\phantom{-}e^{6} - 10e^{4} - 2e^{3} + 19e^{2} + 4e - 6$
11 $[11, 11, 3w - 20]$ $\phantom{-}e^{6} - 10e^{4} - 2e^{3} + 19e^{2} + 4e - 6$
13 $[13, 13, 2w - 13]$ $-e^{6} + e^{5} + 9e^{4} - 8e^{3} - 12e^{2} + 15e + 1$
13 $[13, 13, 2w + 11]$ $-e^{6} + e^{5} + 9e^{4} - 8e^{3} - 12e^{2} + 15e + 1$
17 $[17, 17, w + 7]$ $-e^{6} + e^{5} + 10e^{4} - 8e^{3} - 20e^{2} + 13e + 5$
17 $[17, 17, -w + 8]$ $-e^{6} + e^{5} + 10e^{4} - 8e^{3} - 20e^{2} + 13e + 5$
19 $[19, 19, -w - 4]$ $-2e^{5} + e^{4} + 18e^{3} - 4e^{2} - 24e$
19 $[19, 19, -w + 5]$ $-2e^{5} + e^{4} + 18e^{3} - 4e^{2} - 24e$
25 $[25, 5, 5]$ $-2e^{5} + 19e^{3} + 4e^{2} - 29e$
31 $[31, 31, -6w - 35]$ $\phantom{-}2e^{6} - 2e^{5} - 18e^{4} + 14e^{3} + 24e^{2} - 16e$
31 $[31, 31, -6w + 41]$ $\phantom{-}2e^{6} - 2e^{5} - 18e^{4} + 14e^{3} + 24e^{2} - 16e$
37 $[37, 37, -w - 1]$ $-e^{6} + 3e^{5} + 9e^{4} - 26e^{3} - 16e^{2} + 35e + 3$
37 $[37, 37, w - 2]$ $-e^{6} + 3e^{5} + 9e^{4} - 26e^{3} - 16e^{2} + 35e + 3$
47 $[47, 47, 3w + 16]$ $\phantom{-}2e^{5} - 18e^{3} - 4e^{2} + 20e + 6$
47 $[47, 47, -3w + 19]$ $\phantom{-}2e^{5} - 18e^{3} - 4e^{2} + 20e + 6$
49 $[49, 7, -7]$ $\phantom{-}3e^{5} - e^{4} - 28e^{3} + 3e^{2} + 39e + 7$
67 $[67, 67, 3w - 22]$ $\phantom{-}2e^{6} - 2e^{5} - 18e^{4} + 14e^{3} + 25e^{2} - 16e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $1$