Properties

Base field \(\Q(\sqrt{67}) \)
Weight [2, 2]
Level norm 14
Level $[14,14,w + 9]$
Label 2.2.268.1-14.2-e
Dimension 13
CM no
Base change no

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Base field \(\Q(\sqrt{67}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 67\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2]
Level $[14,14,w + 9]$
Label 2.2.268.1-14.2-e
Dimension 13
Is CM no
Is base change no
Parent newspace dimension 68

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{13} \) \(\mathstrut -\mathstrut 25x^{11} \) \(\mathstrut +\mathstrut 6x^{10} \) \(\mathstrut +\mathstrut 235x^{9} \) \(\mathstrut -\mathstrut 113x^{8} \) \(\mathstrut -\mathstrut 999x^{7} \) \(\mathstrut +\mathstrut 712x^{6} \) \(\mathstrut +\mathstrut 1729x^{5} \) \(\mathstrut -\mathstrut 1601x^{4} \) \(\mathstrut -\mathstrut 564x^{3} \) \(\mathstrut +\mathstrut 618x^{2} \) \(\mathstrut +\mathstrut 47x \) \(\mathstrut -\mathstrut 64\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -27w + 221]$ $\phantom{-}1$
3 $[3, 3, -w + 8]$ $...$
3 $[3, 3, -w - 8]$ $\phantom{-}e$
7 $[7, 7, -11w + 90]$ $-1$
7 $[7, 7, -11w - 90]$ $...$
11 $[11, 11, 6w - 49]$ $...$
11 $[11, 11, 6w + 49]$ $...$
17 $[17, 17, 4w + 33]$ $...$
17 $[17, 17, -4w + 33]$ $...$
25 $[25, 5, -5]$ $...$
29 $[29, 29, -70w + 573]$ $...$
29 $[29, 29, 151w - 1236]$ $...$
31 $[31, 31, -w - 6]$ $...$
31 $[31, 31, w - 6]$ $...$
37 $[37, 37, -21w - 172]$ $...$
37 $[37, 37, -21w + 172]$ $...$
43 $[43, 43, 2w - 15]$ $...$
43 $[43, 43, 2w + 15]$ $...$
67 $[67, 67, -w]$ $...$
73 $[73, 73, -3w - 26]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,27w + 221]$ $-1$
7 $[7,7,11w - 90]$ $1$