Properties

Base field \(\Q(\sqrt{393}) \)
Weight [2, 2]
Level norm 3
Level $[3, 3, -842w + 8767]$
Label 2.2.393.1-3.1-a
Dimension 2
CM no
Base change no

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Base field \(\Q(\sqrt{393}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 98\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2]
Level $[3, 3, -842w + 8767]$
Label 2.2.393.1-3.1-a
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 42

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} \) \(\mathstrut -\mathstrut 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -17w - 160]$ $\phantom{-}0$
2 $[2, 2, -17w + 177]$ $\phantom{-}e$
3 $[3, 3, -842w + 8767]$ $-1$
7 $[7, 7, -2w + 21]$ $-3$
7 $[7, 7, 2w + 19]$ $\phantom{-}2$
13 $[13, 13, -12w - 113]$ $-4$
13 $[13, 13, 12w - 125]$ $\phantom{-}6$
17 $[17, 17, 182w - 1895]$ $\phantom{-}2e$
17 $[17, 17, 182w + 1713]$ $\phantom{-}2e$
23 $[23, 23, -512w - 4819]$ $\phantom{-}0$
23 $[23, 23, 512w - 5331]$ $\phantom{-}2e$
25 $[25, 5, -5]$ $\phantom{-}4$
29 $[29, 29, 22w - 229]$ $-2e$
29 $[29, 29, 22w + 207]$ $-e$
43 $[43, 43, 114w + 1073]$ $\phantom{-}1$
43 $[43, 43, 114w - 1187]$ $\phantom{-}6$
47 $[47, 47, 8w - 83]$ $\phantom{-}4e$
47 $[47, 47, -8w - 75]$ $-5e$
61 $[61, 61, -1172w - 11031]$ $\phantom{-}8$
61 $[61, 61, 1172w - 12203]$ $-2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -842w + 8767]$ $1$