Properties

Base field \(\Q(\sqrt{393}) \)
Weight [2, 2]
Level norm 6
Level $[6, 6, -5w - 47]$
Label 2.2.393.1-6.1-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 $[6, 6, -5w - 47]$
Label 2.2.393.1-6.1-a
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 44

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} \) \(\mathstrut +\mathstrut 2x \) \(\mathstrut -\mathstrut 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -17w - 160]$ $\phantom{-}1$
2 $[2, 2, -17w + 177]$ $\phantom{-}1$
3 $[3, 3, -842w + 8767]$ $\phantom{-}1$
7 $[7, 7, -2w + 21]$ $\phantom{-}e$
7 $[7, 7, 2w + 19]$ $\phantom{-}0$
13 $[13, 13, -12w - 113]$ $-\frac{1}{2}e - 1$
13 $[13, 13, 12w - 125]$ $\phantom{-}\frac{1}{2}e - 1$
17 $[17, 17, 182w - 1895]$ $-\frac{1}{2}e - 5$
17 $[17, 17, 182w + 1713]$ $\phantom{-}\frac{3}{2}e + 1$
23 $[23, 23, -512w - 4819]$ $\phantom{-}e + 2$
23 $[23, 23, 512w - 5331]$ $-e - 2$
25 $[25, 5, -5]$ $\phantom{-}e + 2$
29 $[29, 29, 22w - 229]$ $-\frac{1}{2}e + 5$
29 $[29, 29, 22w + 207]$ $\phantom{-}\frac{1}{2}e - 1$
43 $[43, 43, 114w + 1073]$ $-2$
43 $[43, 43, 114w - 1187]$ $\phantom{-}e - 2$
47 $[47, 47, 8w - 83]$ $\phantom{-}e + 6$
47 $[47, 47, -8w - 75]$ $\phantom{-}10$
61 $[61, 61, -1172w - 11031]$ $\phantom{-}\frac{1}{2}e + 7$
61 $[61, 61, 1172w - 12203]$ $-\frac{5}{2}e - 1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -17w + 177]$ $-1$
3 $[3, 3, -842w + 8767]$ $-1$