Properties

Base field \(\Q(\sqrt{393}) \)
Weight [2, 2]
Level norm 3
Level $[3, 3, -842w + 8767]$
Label 2.2.393.1-3.1-j
Dimension 10
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-j
Dimension 10
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:
\(x^{10} \) \(\mathstrut -\mathstrut 18x^{8} \) \(\mathstrut +\mathstrut 115x^{6} \) \(\mathstrut -\mathstrut 314x^{4} \) \(\mathstrut +\mathstrut 335x^{2} \) \(\mathstrut -\mathstrut 91\)

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Norm Prime Eigenvalue
2 $[2, 2, -17w - 160]$ $-e$
2 $[2, 2, -17w + 177]$ $\phantom{-}e$
3 $[3, 3, -842w + 8767]$ $\phantom{-}1$
7 $[7, 7, -2w + 21]$ $-\frac{4}{19}e^{8} + \frac{51}{19}e^{6} - \frac{178}{19}e^{4} + \frac{141}{19}e^{2} - \frac{6}{19}$
7 $[7, 7, 2w + 19]$ $-\frac{4}{19}e^{8} + \frac{51}{19}e^{6} - \frac{178}{19}e^{4} + \frac{141}{19}e^{2} - \frac{6}{19}$
13 $[13, 13, -12w - 113]$ $\phantom{-}\frac{10}{19}e^{8} - \frac{137}{19}e^{6} + \frac{559}{19}e^{4} - \frac{723}{19}e^{2} + \frac{224}{19}$
13 $[13, 13, 12w - 125]$ $\phantom{-}\frac{10}{19}e^{8} - \frac{137}{19}e^{6} + \frac{559}{19}e^{4} - \frac{723}{19}e^{2} + \frac{224}{19}$
17 $[17, 17, 182w - 1895]$ $-\frac{5}{19}e^{9} + \frac{78}{19}e^{7} - \frac{403}{19}e^{5} + \frac{789}{19}e^{3} - \frac{416}{19}e$
17 $[17, 17, 182w + 1713]$ $\phantom{-}\frac{5}{19}e^{9} - \frac{78}{19}e^{7} + \frac{403}{19}e^{5} - \frac{789}{19}e^{3} + \frac{416}{19}e$
23 $[23, 23, -512w - 4819]$ $-\frac{3}{19}e^{9} + \frac{43}{19}e^{7} - \frac{181}{19}e^{5} + \frac{196}{19}e^{3} + \frac{43}{19}e$
23 $[23, 23, 512w - 5331]$ $\phantom{-}\frac{3}{19}e^{9} - \frac{43}{19}e^{7} + \frac{181}{19}e^{5} - \frac{196}{19}e^{3} - \frac{43}{19}e$
25 $[25, 5, -5]$ $\phantom{-}\frac{7}{19}e^{8} - \frac{94}{19}e^{6} + \frac{359}{19}e^{4} - \frac{356}{19}e^{2} - \frac{94}{19}$
29 $[29, 29, 22w - 229]$ $-\frac{3}{19}e^{9} + \frac{43}{19}e^{7} - \frac{200}{19}e^{5} + \frac{367}{19}e^{3} - \frac{242}{19}e$
29 $[29, 29, 22w + 207]$ $\phantom{-}\frac{3}{19}e^{9} - \frac{43}{19}e^{7} + \frac{200}{19}e^{5} - \frac{367}{19}e^{3} + \frac{242}{19}e$
43 $[43, 43, 114w + 1073]$ $-\frac{21}{19}e^{8} + \frac{301}{19}e^{6} - \frac{1343}{19}e^{4} + \frac{2018}{19}e^{2} - \frac{649}{19}$
43 $[43, 43, 114w - 1187]$ $-\frac{21}{19}e^{8} + \frac{301}{19}e^{6} - \frac{1343}{19}e^{4} + \frac{2018}{19}e^{2} - \frac{649}{19}$
47 $[47, 47, 8w - 83]$ $\phantom{-}\frac{9}{19}e^{9} - \frac{129}{19}e^{7} + \frac{562}{19}e^{5} - \frac{740}{19}e^{3} + \frac{4}{19}e$
47 $[47, 47, -8w - 75]$ $-\frac{9}{19}e^{9} + \frac{129}{19}e^{7} - \frac{562}{19}e^{5} + \frac{740}{19}e^{3} - \frac{4}{19}e$
61 $[61, 61, -1172w - 11031]$ $\phantom{-}\frac{9}{19}e^{8} - \frac{110}{19}e^{6} + \frac{353}{19}e^{4} - \frac{208}{19}e^{2} - \frac{91}{19}$
61 $[61, 61, 1172w - 12203]$ $\phantom{-}\frac{9}{19}e^{8} - \frac{110}{19}e^{6} + \frac{353}{19}e^{4} - \frac{208}{19}e^{2} - \frac{91}{19}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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