Properties

Base field \(\Q(\sqrt{393}) \)
Weight [2, 2]
Level norm 6
Level $[6, 6, -5w - 47]$
Label 2.2.393.1-6.1-f
Dimension 7
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-f
Dimension 7
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:
\(x^{7} \) \(\mathstrut -\mathstrut 12x^{5} \) \(\mathstrut -\mathstrut x^{4} \) \(\mathstrut +\mathstrut 40x^{3} \) \(\mathstrut +\mathstrut 6x^{2} \) \(\mathstrut -\mathstrut 28x \) \(\mathstrut -\mathstrut 8\)

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Norm Prime Eigenvalue
2 $[2, 2, -17w - 160]$ $\phantom{-}e$
2 $[2, 2, -17w + 177]$ $-1$
3 $[3, 3, -842w + 8767]$ $-1$
7 $[7, 7, -2w + 21]$ $-\frac{1}{4}e^{6} + 3e^{4} - \frac{3}{4}e^{3} - 10e^{2} + \frac{9}{2}e + 6$
7 $[7, 7, 2w + 19]$ $\phantom{-}\frac{1}{2}e^{5} - 4e^{3} - \frac{1}{2}e^{2} + 6e + 1$
13 $[13, 13, -12w - 113]$ $\phantom{-}\frac{1}{4}e^{6} - 3e^{4} + \frac{3}{4}e^{3} + 10e^{2} - \frac{9}{2}e - 7$
13 $[13, 13, 12w - 125]$ $\phantom{-}\frac{1}{4}e^{6} - 2e^{4} - \frac{5}{4}e^{3} + 3e^{2} + \frac{11}{2}e - 1$
17 $[17, 17, 182w - 1895]$ $-\frac{1}{4}e^{6} + \frac{1}{2}e^{5} + 3e^{4} - \frac{19}{4}e^{3} - \frac{19}{2}e^{2} + \frac{19}{2}e + 6$
17 $[17, 17, 182w + 1713]$ $-\frac{1}{4}e^{6} + 4e^{4} - \frac{3}{4}e^{3} - 16e^{2} + \frac{7}{2}e + 9$
23 $[23, 23, -512w - 4819]$ $\phantom{-}\frac{1}{2}e^{5} - 4e^{3} - \frac{1}{2}e^{2} + 8e + 1$
23 $[23, 23, 512w - 5331]$ $\phantom{-}\frac{1}{4}e^{6} - 3e^{4} - \frac{1}{4}e^{3} + 11e^{2} + \frac{1}{2}e - 9$
25 $[25, 5, -5]$ $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + 5e^{4} - \frac{7}{2}e^{3} - \frac{27}{2}e^{2} + 5e + 9$
29 $[29, 29, 22w - 229]$ $\phantom{-}\frac{3}{4}e^{6} - \frac{1}{2}e^{5} - 9e^{4} + \frac{17}{4}e^{3} + \frac{57}{2}e^{2} - \frac{15}{2}e - 12$
29 $[29, 29, 22w + 207]$ $\phantom{-}\frac{1}{2}e^{5} - 4e^{3} - \frac{1}{2}e^{2} + 4e + 4$
43 $[43, 43, 114w + 1073]$ $-\frac{1}{2}e^{6} + 5e^{4} + \frac{3}{2}e^{3} - 14e^{2} - 6e + 9$
43 $[43, 43, 114w - 1187]$ $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - 4e^{4} + \frac{7}{2}e^{3} + \frac{17}{2}e^{2} - 5e - 13$
47 $[47, 47, 8w - 83]$ $\phantom{-}\frac{1}{4}e^{6} - 2e^{4} - \frac{1}{4}e^{3} + 2e^{2} - \frac{3}{2}e + 5$
47 $[47, 47, -8w - 75]$ $-\frac{1}{4}e^{6} + 3e^{4} - \frac{3}{4}e^{3} - 10e^{2} + \frac{5}{2}e + 10$
61 $[61, 61, -1172w - 11031]$ $\phantom{-}\frac{1}{4}e^{6} + \frac{1}{2}e^{5} - 4e^{4} - \frac{13}{4}e^{3} + \frac{33}{2}e^{2} + \frac{3}{2}e - 12$
61 $[61, 61, 1172w - 12203]$ $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + 6e^{4} - \frac{9}{2}e^{3} - \frac{41}{2}e^{2} + 7e + 17$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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