Properties

Base field \(\Q(\sqrt{393}) \)
Weight [2, 2]
Level norm 2
Level $[2,2,17w - 177]$
Label 2.2.393.1-2.2-a
Dimension 6
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 $[2,2,17w - 177]$
Label 2.2.393.1-2.2-a
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 12

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut x^{5} \) \(\mathstrut -\mathstrut 7x^{4} \) \(\mathstrut +\mathstrut 2x^{3} \) \(\mathstrut +\mathstrut 14x^{2} \) \(\mathstrut +\mathstrut 5x \) \(\mathstrut -\mathstrut 1\)

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Norm Prime Eigenvalue
2 $[2, 2, -17w - 160]$ $\phantom{-}e^{5} - 2e^{4} - 5e^{3} + 6e^{2} + 8e$
2 $[2, 2, -17w + 177]$ $\phantom{-}1$
3 $[3, 3, -842w + 8767]$ $\phantom{-}e$
7 $[7, 7, -2w + 21]$ $\phantom{-}2e^{5} - 5e^{4} - 6e^{3} + 14e^{2} + 6e - 2$
7 $[7, 7, 2w + 19]$ $\phantom{-}e^{4} - 3e^{3} - 3e^{2} + 8e + 3$
13 $[13, 13, -12w - 113]$ $\phantom{-}e^{5} - 3e^{4} - 5e^{3} + 12e^{2} + 9e - 6$
13 $[13, 13, 12w - 125]$ $\phantom{-}e^{4} - 6e^{2} - 2e + 5$
17 $[17, 17, 182w - 1895]$ $-2e^{5} + 3e^{4} + 11e^{3} - 10e^{2} - 16e + 1$
17 $[17, 17, 182w + 1713]$ $\phantom{-}e^{5} - 2e^{4} - 3e^{3} + 5e^{2} + e - 4$
23 $[23, 23, -512w - 4819]$ $-3e^{5} + 6e^{4} + 11e^{3} - 15e^{2} - 13e$
23 $[23, 23, 512w - 5331]$ $-2e^{4} + 3e^{3} + 8e^{2} - 7e - 8$
25 $[25, 5, -5]$ $-3e^{5} + 7e^{4} + 13e^{3} - 22e^{2} - 20e + 1$
29 $[29, 29, 22w - 229]$ $-2e^{5} + 2e^{4} + 14e^{3} - 7e^{2} - 26e - 5$
29 $[29, 29, 22w + 207]$ $\phantom{-}2e^{5} - 5e^{4} - 6e^{3} + 15e^{2} + 2e - 6$
43 $[43, 43, 114w + 1073]$ $-e^{5} + e^{4} + 4e^{3} - 2e^{2} - 4e + 5$
43 $[43, 43, 114w - 1187]$ $\phantom{-}4e^{4} - 8e^{3} - 13e^{2} + 21e + 9$
47 $[47, 47, 8w - 83]$ $-4e^{5} + 11e^{4} + 10e^{3} - 30e^{2} - 9e + 3$
47 $[47, 47, -8w - 75]$ $\phantom{-}2e^{5} - 2e^{4} - 9e^{3} + 5e^{2} + 5e - 2$
61 $[61, 61, -1172w - 11031]$ $-10e^{5} + 19e^{4} + 46e^{3} - 53e^{2} - 65e$
61 $[61, 61, 1172w - 12203]$ $\phantom{-}e^{5} - 6e^{3} - 3e^{2} + 10e + 3$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,17w - 177]$ $-1$