Properties

Label 2.2.377.1-2.1-i
Base field \(\Q(\sqrt{377}) \)
Weight $[2, 2]$
Level norm $2$
Level $[2, 2, w]$
Dimension $4$
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: $[2, 2, w]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $24$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 3x^{2} + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $-e^{3} - 2e$
2 $[2, 2, w + 1]$ $\phantom{-}e$
9 $[9, 3, 3]$ $\phantom{-}e^{2} - 1$
11 $[11, 11, w + 2]$ $\phantom{-}3e^{3} + 7e$
11 $[11, 11, w + 8]$ $\phantom{-}5e^{3} + 10e$
13 $[13, 13, 4w - 41]$ $\phantom{-}e^{2} + 3$
19 $[19, 19, w + 7]$ $-2e^{3} - 5e$
19 $[19, 19, w + 11]$ $\phantom{-}e^{3} + 7e$
23 $[23, 23, -2w + 21]$ $\phantom{-}e^{2} - 2$
23 $[23, 23, -2w - 19]$ $\phantom{-}2e^{2} + 7$
25 $[25, 5, -5]$ $-4e^{2} - 5$
29 $[29, 29, 6w - 61]$ $-2e^{2} - 3$
31 $[31, 31, w + 12]$ $-e^{3} + e$
31 $[31, 31, w + 18]$ $\phantom{-}2e^{3} + 8e$
37 $[37, 37, w + 4]$ $\phantom{-}e^{3}$
37 $[37, 37, w + 32]$ $-5e^{3} - 14e$
41 $[41, 41, w + 3]$ $\phantom{-}e^{3} + 4e$
41 $[41, 41, w + 37]$ $\phantom{-}7e^{3} + 13e$
47 $[47, 47, w]$ $-2e^{3} - 2e$
47 $[47, 47, w + 46]$ $-9e^{3} - 20e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $e^{3} + 2e$