Properties

Base field \(\Q(\sqrt{109}) \)
Weight [2, 2]
Level norm 4
Level $[4, 2, 2]$
Label 2.2.109.1-4.1-b
Dimension 5
CM no
Base change yes

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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 $[4, 2, 2]$
Label 2.2.109.1-4.1-b
Dimension 5
Is CM no
Is base change yes
Parent newspace dimension 7

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} \) \(\mathstrut +\mathstrut x^{4} \) \(\mathstrut -\mathstrut 11x^{3} \) \(\mathstrut -\mathstrut 12x^{2} \) \(\mathstrut +\mathstrut 16x \) \(\mathstrut +\mathstrut 2\)

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Norm Prime Eigenvalue
3 $[3, 3, -w + 6]$ $\phantom{-}e$
3 $[3, 3, w + 5]$ $\phantom{-}e$
4 $[4, 2, 2]$ $-1$
5 $[5, 5, -3w + 17]$ $-e^{4} + e^{3} + 8e^{2} - 3e - 3$
5 $[5, 5, -3w - 14]$ $-e^{4} + e^{3} + 8e^{2} - 3e - 3$
7 $[7, 7, w - 5]$ $-e^{3} + e^{2} + 7e - 2$
7 $[7, 7, w + 4]$ $-e^{3} + e^{2} + 7e - 2$
29 $[29, 29, -w - 7]$ $-2e^{4} + 2e^{3} + 15e^{2} - 5e - 1$
29 $[29, 29, -w + 8]$ $-2e^{4} + 2e^{3} + 15e^{2} - 5e - 1$
31 $[31, 31, -5w + 28]$ $\phantom{-}e^{3} - e^{2} - 9e$
31 $[31, 31, -5w - 23]$ $\phantom{-}e^{3} - e^{2} - 9e$
43 $[43, 43, 6w + 29]$ $\phantom{-}2e^{4} - 3e^{3} - 14e^{2} + 13e - 4$
43 $[43, 43, -6w + 35]$ $\phantom{-}2e^{4} - 3e^{3} - 14e^{2} + 13e - 4$
61 $[61, 61, 3w - 19]$ $-e^{4} + e^{3} + 10e^{2} - 3e - 9$
61 $[61, 61, -3w - 16]$ $-e^{4} + e^{3} + 10e^{2} - 3e - 9$
71 $[71, 71, -7w - 34]$ $\phantom{-}3e^{3} - 3e^{2} - 23e + 10$
71 $[71, 71, 7w - 41]$ $\phantom{-}3e^{3} - 3e^{2} - 23e + 10$
73 $[73, 73, 2w - 7]$ $\phantom{-}e^{4} - e^{3} - 8e^{2} + 6e + 1$
73 $[73, 73, -2w - 5]$ $\phantom{-}e^{4} - e^{3} - 8e^{2} + 6e + 1$
83 $[83, 83, -w - 10]$ $-e^{4} - e^{3} + 10e^{2} + 10e - 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $1$