Properties

Base field \(\Q(\sqrt{67}) \)
Weight [2, 2]
Level norm 3
Level $[3,3,w + 8]$
Label 2.2.268.1-3.2-d
Dimension 7
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 $[3,3,w + 8]$
Label 2.2.268.1-3.2-d
Dimension 7
Is CM no
Is base change no
Parent newspace dimension 16

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} \) \(\mathstrut +\mathstrut 2x^{6} \) \(\mathstrut -\mathstrut 6x^{5} \) \(\mathstrut -\mathstrut 12x^{4} \) \(\mathstrut +\mathstrut 9x^{3} \) \(\mathstrut +\mathstrut 18x^{2} \) \(\mathstrut -\mathstrut 4x \) \(\mathstrut -\mathstrut 7\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -27w + 221]$ $\phantom{-}e$
3 $[3, 3, -w + 8]$ $\phantom{-}e^{6} + e^{5} - 6e^{4} - 4e^{3} + 8e^{2} + e - 2$
3 $[3, 3, -w - 8]$ $\phantom{-}1$
7 $[7, 7, -11w + 90]$ $-2e^{6} + 15e^{4} - e^{3} - 32e^{2} + 3e + 17$
7 $[7, 7, -11w - 90]$ $\phantom{-}2e^{6} + e^{5} - 13e^{4} - 4e^{3} + 23e^{2} + e - 12$
11 $[11, 11, 6w - 49]$ $\phantom{-}e^{6} + 3e^{5} - 5e^{4} - 15e^{3} + 4e^{2} + 12e + 1$
11 $[11, 11, 6w + 49]$ $-e^{6} - 2e^{5} + 5e^{4} + 9e^{3} - 5e^{2} - 5e$
17 $[17, 17, 4w + 33]$ $-4e^{6} - 4e^{5} + 24e^{4} + 20e^{3} - 34e^{2} - 17e + 10$
17 $[17, 17, -4w + 33]$ $-e^{6} - e^{5} + 7e^{4} + 4e^{3} - 15e^{2} - 2e + 11$
25 $[25, 5, -5]$ $-e^{6} + 7e^{4} - 2e^{3} - 13e^{2} + 5e + 2$
29 $[29, 29, -70w + 573]$ $-2e^{5} - e^{4} + 13e^{3} + 5e^{2} - 16e - 5$
29 $[29, 29, 151w - 1236]$ $-5e^{6} - 5e^{5} + 29e^{4} + 22e^{3} - 35e^{2} - 12e + 3$
31 $[31, 31, -w - 6]$ $-e^{5} + 6e^{3} - 7e - 5$
31 $[31, 31, w - 6]$ $\phantom{-}4e^{6} + 3e^{5} - 26e^{4} - 16e^{3} + 44e^{2} + 19e - 18$
37 $[37, 37, -21w - 172]$ $-2e^{6} - 2e^{5} + 10e^{4} + 7e^{3} - 4e^{2} + 3e - 7$
37 $[37, 37, -21w + 172]$ $\phantom{-}3e^{6} + 3e^{5} - 20e^{4} - 14e^{3} + 35e^{2} + 8e - 16$
43 $[43, 43, 2w - 15]$ $-3e^{6} - 3e^{5} + 19e^{4} + 16e^{3} - 33e^{2} - 17e + 15$
43 $[43, 43, 2w + 15]$ $\phantom{-}e^{6} - e^{5} - 10e^{4} + 3e^{3} + 26e^{2} + 3e - 18$
67 $[67, 67, -w]$ $\phantom{-}5e^{6} + 6e^{5} - 27e^{4} - 29e^{3} + 32e^{2} + 22e - 14$
73 $[73, 73, -3w - 26]$ $\phantom{-}e^{6} - 6e^{4} + 8e^{2} - 3e - 3$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3,3,w + 8]$ $-1$