Properties

Base field \(\Q(\sqrt{157}) \)
Weight [2, 2]
Level norm 12
Level $[12,6,-2w + 14]$
Label 2.2.157.1-12.2-h
Dimension 6
CM no
Base change no

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Base field \(\Q(\sqrt{157}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 39\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[12,6,-2w + 14]$
Label 2.2.157.1-12.2-h
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 22

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut +\mathstrut x^{5} \) \(\mathstrut -\mathstrut 10x^{4} \) \(\mathstrut -\mathstrut 3x^{3} \) \(\mathstrut +\mathstrut 16x^{2} \) \(\mathstrut -\mathstrut 1\)

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Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $\phantom{-}e$
3 $[3, 3, -w + 7]$ $\phantom{-}1$
4 $[4, 2, 2]$ $\phantom{-}1$
11 $[11, 11, -3w - 17]$ $-\frac{3}{5}e^{5} - \frac{4}{5}e^{4} + \frac{27}{5}e^{3} + \frac{13}{5}e^{2} - \frac{27}{5}e + \frac{6}{5}$
11 $[11, 11, 3w - 20]$ $-\frac{2}{5}e^{5} - \frac{1}{5}e^{4} + \frac{23}{5}e^{3} - \frac{3}{5}e^{2} - \frac{48}{5}e + \frac{14}{5}$
13 $[13, 13, 2w - 13]$ $\phantom{-}\frac{2}{5}e^{5} + \frac{1}{5}e^{4} - \frac{23}{5}e^{3} - \frac{2}{5}e^{2} + \frac{43}{5}e + \frac{1}{5}$
13 $[13, 13, 2w + 11]$ $-\frac{8}{5}e^{5} - \frac{9}{5}e^{4} + \frac{77}{5}e^{3} + \frac{33}{5}e^{2} - \frac{107}{5}e - \frac{9}{5}$
17 $[17, 17, w + 7]$ $-\frac{11}{5}e^{5} - \frac{13}{5}e^{4} + \frac{104}{5}e^{3} + \frac{46}{5}e^{2} - \frac{144}{5}e - \frac{3}{5}$
17 $[17, 17, -w + 8]$ $\phantom{-}\frac{4}{5}e^{5} + \frac{2}{5}e^{4} - \frac{41}{5}e^{3} + \frac{6}{5}e^{2} + \frac{61}{5}e + \frac{2}{5}$
19 $[19, 19, -w - 4]$ $\phantom{-}e^{5} + e^{4} - 10e^{3} - 3e^{2} + 18e + 1$
19 $[19, 19, -w + 5]$ $\phantom{-}e^{3} + 2e^{2} - 7e - 5$
25 $[25, 5, 5]$ $\phantom{-}\frac{2}{5}e^{5} + \frac{1}{5}e^{4} - \frac{18}{5}e^{3} + \frac{3}{5}e^{2} + \frac{13}{5}e - \frac{4}{5}$
31 $[31, 31, -6w - 35]$ $\phantom{-}\frac{7}{5}e^{5} + \frac{6}{5}e^{4} - \frac{73}{5}e^{3} - \frac{17}{5}e^{2} + \frac{128}{5}e + \frac{16}{5}$
31 $[31, 31, -6w + 41]$ $\phantom{-}\frac{4}{5}e^{5} + \frac{7}{5}e^{4} - \frac{31}{5}e^{3} - \frac{34}{5}e^{2} + \frac{21}{5}e + \frac{27}{5}$
37 $[37, 37, -w - 1]$ $\phantom{-}\frac{1}{5}e^{5} + \frac{3}{5}e^{4} - \frac{9}{5}e^{3} - \frac{21}{5}e^{2} + \frac{14}{5}e + \frac{28}{5}$
37 $[37, 37, w - 2]$ $\phantom{-}e^{5} + e^{4} - 10e^{3} - 4e^{2} + 16e$
47 $[47, 47, 3w + 16]$ $\phantom{-}\frac{9}{5}e^{5} + \frac{12}{5}e^{4} - \frac{86}{5}e^{3} - \frac{49}{5}e^{2} + \frac{141}{5}e - \frac{3}{5}$
47 $[47, 47, -3w + 19]$ $-e^{5} + 11e^{3} - 5e^{2} - 18e + 4$
49 $[49, 7, -7]$ $\phantom{-}\frac{3}{5}e^{5} + \frac{4}{5}e^{4} - \frac{32}{5}e^{3} - \frac{23}{5}e^{2} + \frac{57}{5}e + \frac{19}{5}$
67 $[67, 67, 3w - 22]$ $\phantom{-}\frac{3}{5}e^{5} + \frac{14}{5}e^{4} - \frac{17}{5}e^{3} - \frac{108}{5}e^{2} + \frac{7}{5}e + \frac{84}{5}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3,3,-w + 7]$ $-1$
4 $[4,2,2]$ $-1$