Properties

Base field \(\Q(\sqrt{34}) \)
Weight [2, 2]
Level norm 1
Level $[1, 1, 1]$
Label 2.2.136.1-1.1-b
Dimension 8
CM no
Base change no

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Base field \(\Q(\sqrt{34}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 34\); narrow class number \(4\) and class number \(2\).

Form

Weight [2, 2]
Level $[1, 1, 1]$
Label 2.2.136.1-1.1-b
Dimension 8
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:
\(x^{8} \) \(\mathstrut +\mathstrut 14x^{6} \) \(\mathstrut +\mathstrut 56x^{4} \) \(\mathstrut +\mathstrut 76x^{2} \) \(\mathstrut +\mathstrut 32\)

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Norm Prime Eigenvalue
2 $[2, 2, w - 6]$ $-\frac{1}{4}e^{6} - \frac{7}{2}e^{4} - 13e^{2} - 11$
3 $[3, 3, w + 1]$ $-e$
3 $[3, 3, w + 2]$ $\phantom{-}e$
5 $[5, 5, w + 2]$ $-\frac{1}{4}e^{7} - 3e^{5} - 8e^{3} - 3e$
5 $[5, 5, w + 3]$ $\phantom{-}\frac{1}{4}e^{7} + 3e^{5} + 8e^{3} + 3e$
11 $[11, 11, w + 1]$ $-e^{7} - 13e^{5} - 43e^{3} - 33e$
11 $[11, 11, w + 10]$ $\phantom{-}e^{7} + 13e^{5} + 43e^{3} + 33e$
17 $[17, 17, -3w + 17]$ $-e^{6} - 12e^{4} - 34e^{2} - 22$
29 $[29, 29, w + 11]$ $\phantom{-}\frac{3}{4}e^{7} + 10e^{5} + 34e^{3} + 25e$
29 $[29, 29, w + 18]$ $-\frac{3}{4}e^{7} - 10e^{5} - 34e^{3} - 25e$
37 $[37, 37, w + 16]$ $-\frac{5}{4}e^{7} - 16e^{5} - 52e^{3} - 41e$
37 $[37, 37, w + 21]$ $\phantom{-}\frac{5}{4}e^{7} + 16e^{5} + 52e^{3} + 41e$
47 $[47, 47, -w - 9]$ $-\frac{1}{2}e^{6} - 6e^{4} - 18e^{2} - 16$
47 $[47, 47, w - 9]$ $-\frac{1}{2}e^{6} - 6e^{4} - 18e^{2} - 16$
49 $[49, 7, -7]$ $-e^{6} - 13e^{4} - 43e^{2} - 26$
61 $[61, 61, w + 20]$ $-\frac{5}{4}e^{7} - 16e^{5} - 52e^{3} - 43e$
61 $[61, 61, w + 41]$ $\phantom{-}\frac{5}{4}e^{7} + 16e^{5} + 52e^{3} + 43e$
89 $[89, 89, 2w - 15]$ $\phantom{-}2e^{6} + 25e^{4} + 75e^{2} + 46$
89 $[89, 89, -2w - 15]$ $\phantom{-}2e^{6} + 25e^{4} + 75e^{2} + 46$
103 $[103, 103, -14w + 81]$ $\phantom{-}3e^{6} + 40e^{4} + 138e^{2} + 104$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).