Properties

Label 2.2.377.1-8.2-b
Base field \(\Q(\sqrt{377}) \)
Weight $[2, 2]$
Level norm $8$
Level $[8,4,-2w + 2]$
Dimension $10$
CM no
Base change no

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Base field \(\Q(\sqrt{377}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 94\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[8,4,-2w + 2]$
Dimension: $10$
CM: no
Base change: no
Newspace dimension: $40$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{10} + x^{9} - 42x^{8} - 6x^{7} + 594x^{6} - 424x^{5} - 2735x^{4} + 4203x^{3} - 1180x^{2} - 466x + 172\)

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Norm Prime Eigenvalue
2 $[2, 2, w]$ $-1$
2 $[2, 2, w + 1]$ $\phantom{-}0$
9 $[9, 3, 3]$ $\phantom{-}e$
11 $[11, 11, w + 2]$ $...$
11 $[11, 11, w + 8]$ $...$
13 $[13, 13, 4w - 41]$ $...$
19 $[19, 19, w + 7]$ $...$
19 $[19, 19, w + 11]$ $...$
23 $[23, 23, -2w + 21]$ $...$
23 $[23, 23, -2w - 19]$ $...$
25 $[25, 5, -5]$ $...$
29 $[29, 29, 6w - 61]$ $...$
31 $[31, 31, w + 12]$ $...$
31 $[31, 31, w + 18]$ $...$
37 $[37, 37, w + 4]$ $...$
37 $[37, 37, w + 32]$ $...$
41 $[41, 41, w + 3]$ $...$
41 $[41, 41, w + 37]$ $...$
47 $[47, 47, w]$ $...$
47 $[47, 47, w + 46]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2,2,-w + 1]$ $-1$
$2$ $[2,2,-w + 2]$ $1$