Properties

Base field \(\Q(\sqrt{393}) \)
Weight [2, 2]
Level norm 9
Level $[9, 3, 3]$
Label 2.2.393.1-9.1-h
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-h
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:
\(x^{20} \) \(\mathstrut -\mathstrut 29x^{18} \) \(\mathstrut +\mathstrut 347x^{16} \) \(\mathstrut -\mathstrut 2225x^{14} \) \(\mathstrut +\mathstrut 8342x^{12} \) \(\mathstrut -\mathstrut 18815x^{10} \) \(\mathstrut +\mathstrut 25408x^{8} \) \(\mathstrut -\mathstrut 19951x^{6} \) \(\mathstrut +\mathstrut 8687x^{4} \) \(\mathstrut -\mathstrut 1926x^{2} \) \(\mathstrut +\mathstrut 169\)

  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 $[7, 7, -2w + 21]$ $-\frac{6065}{29858}e^{18} + \frac{87040}{14929}e^{16} - \frac{2054741}{29858}e^{14} + \frac{6467391}{14929}e^{12} - \frac{23638091}{14929}e^{10} + \frac{102811867}{29858}e^{8} - \frac{131280445}{29858}e^{6} + \frac{46846808}{14929}e^{4} - \frac{33840067}{29858}e^{2} + \frac{4654925}{29858}$
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 $[3, 3, -842w + 8767]$ $-1$