Properties

Base field \(\Q(\sqrt{393}) \)
Weight [2, 2]
Level norm 9
Level $[9, 3, 3]$
Label 2.2.393.1-9.1-g
Dimension 20
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 $[9, 3, 3]$
Label 2.2.393.1-9.1-g
Dimension 20
Is CM no
Is base change no
Parent newspace dimension 104

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{20} \) \(\mathstrut -\mathstrut 34x^{18} \) \(\mathstrut +\mathstrut 483x^{16} \) \(\mathstrut -\mathstrut 3726x^{14} \) \(\mathstrut +\mathstrut 16964x^{12} \) \(\mathstrut -\mathstrut 46264x^{10} \) \(\mathstrut +\mathstrut 72948x^{8} \) \(\mathstrut -\mathstrut 60398x^{6} \) \(\mathstrut +\mathstrut 21935x^{4} \) \(\mathstrut -\mathstrut 3328x^{2} \) \(\mathstrut +\mathstrut 169\)

  Show full eigenvalues   Hide large eigenvalues

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

Atkin-Lehner eigenvalues

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