Properties

Base field \(\Q(\sqrt{109}) \)
Weight [2, 2]
Level norm 7
Level $[7,7,-w - 4]$
Label 2.2.109.1-7.2-c
Dimension 6
CM no
Base change no

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Base field \(\Q(\sqrt{109}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 27\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[7,7,-w - 4]$
Label 2.2.109.1-7.2-c
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 13

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut 9x^{4} \) \(\mathstrut +\mathstrut 2x^{3} \) \(\mathstrut +\mathstrut 9x^{2} \) \(\mathstrut +\mathstrut x \) \(\mathstrut -\mathstrut 1\)

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Norm Prime Eigenvalue
3 $[3, 3, -w + 6]$ $\phantom{-}e$
3 $[3, 3, w + 5]$ $\phantom{-}e^{5} - 9e^{3} + 2e^{2} + 8e$
4 $[4, 2, 2]$ $-2e^{5} + e^{4} + 17e^{3} - 13e^{2} - 8e + 2$
5 $[5, 5, -3w + 17]$ $\phantom{-}3e^{5} - 2e^{4} - 26e^{3} + 23e^{2} + 14e - 6$
5 $[5, 5, -3w - 14]$ $-e^{5} + e^{4} + 9e^{3} - 10e^{2} - 6e + 2$
7 $[7, 7, w - 5]$ $-3e^{5} + e^{4} + 26e^{3} - 15e^{2} - 18e + 3$
7 $[7, 7, w + 4]$ $\phantom{-}1$
29 $[29, 29, -w - 7]$ $-3e^{5} + 26e^{3} - 6e^{2} - 17e - 3$
29 $[29, 29, -w + 8]$ $\phantom{-}5e^{5} - 2e^{4} - 43e^{3} + 27e^{2} + 26e - 1$
31 $[31, 31, -5w + 28]$ $-5e^{5} + 4e^{4} + 43e^{3} - 45e^{2} - 19e + 10$
31 $[31, 31, -5w - 23]$ $\phantom{-}e^{5} - e^{4} - 8e^{3} + 11e^{2} - 2e - 6$
43 $[43, 43, 6w + 29]$ $\phantom{-}7e^{5} - 3e^{4} - 61e^{3} + 39e^{2} + 39e - 2$
43 $[43, 43, -6w + 35]$ $\phantom{-}8e^{5} - 5e^{4} - 70e^{3} + 59e^{2} + 42e - 16$
61 $[61, 61, 3w - 19]$ $\phantom{-}7e^{5} - 2e^{4} - 61e^{3} + 32e^{2} + 41e - 5$
61 $[61, 61, -3w - 16]$ $-e^{5} - e^{4} + 10e^{3} + 7e^{2} - 18e - 7$
71 $[71, 71, -7w - 34]$ $-11e^{5} + 6e^{4} + 94e^{3} - 74e^{2} - 45e + 19$
71 $[71, 71, 7w - 41]$ $\phantom{-}7e^{5} - 3e^{4} - 60e^{3} + 40e^{2} + 31e - 5$
73 $[73, 73, 2w - 7]$ $\phantom{-}3e^{5} - 2e^{4} - 24e^{3} + 26e^{2} - e - 12$
73 $[73, 73, -2w - 5]$ $\phantom{-}7e^{5} - 2e^{4} - 61e^{3} + 31e^{2} + 44e - 8$
83 $[83, 83, -w - 10]$ $\phantom{-}2e^{5} - 2e^{4} - 15e^{3} + 20e^{2} - 10e - 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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