Properties

Base field \(\Q(\sqrt{113}) \)
Weight [2, 2]
Level norm 9
Level $[9, 3, 3]$
Label 2.2.113.1-9.1-e
Dimension 6
CM no
Base change no

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Base field \(\Q(\sqrt{113}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 28\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[9, 3, 3]$
Label 2.2.113.1-9.1-e
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 24

Hecke eigenvalues ($q$-expansion)

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

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Norm Prime Eigenvalue
2 $[2, 2, -w + 6]$ $\phantom{-}e$
2 $[2, 2, w + 5]$ $-e^{5} - 2e^{4} + 6e^{3} + 10e^{2} - 5e - 6$
7 $[7, 7, 6w - 35]$ $-e^{5} - 2e^{4} + 5e^{3} + 9e^{2} - 3$
7 $[7, 7, -6w - 29]$ $\phantom{-}3e^{5} + 5e^{4} - 18e^{3} - 23e^{2} + 12e + 9$
9 $[9, 3, 3]$ $\phantom{-}1$
11 $[11, 11, 4w + 19]$ $-3e^{5} - 5e^{4} + 18e^{3} + 23e^{2} - 13e - 12$
11 $[11, 11, 4w - 23]$ $\phantom{-}2e^{5} + 4e^{4} - 11e^{3} - 19e^{2} + 5e + 6$
13 $[13, 13, -2w + 11]$ $-e^{5} - e^{4} + 7e^{3} + 3e^{2} - 10e + 2$
13 $[13, 13, 2w + 9]$ $\phantom{-}2e^{5} + 4e^{4} - 12e^{3} - 19e^{2} + 10e + 10$
25 $[25, 5, -5]$ $-3e^{5} - 5e^{4} + 19e^{3} + 24e^{2} - 16e - 11$
31 $[31, 31, 2w - 13]$ $\phantom{-}4e^{5} + 5e^{4} - 27e^{3} - 21e^{2} + 30e + 8$
31 $[31, 31, -2w - 11]$ $\phantom{-}e^{5} - 8e^{3} + e^{2} + 10e$
41 $[41, 41, -8w - 39]$ $-e^{4} + 9e^{2} - 2e - 14$
41 $[41, 41, 8w - 47]$ $-4e^{5} - 6e^{4} + 25e^{3} + 25e^{2} - 18e - 6$
53 $[53, 53, -26w - 125]$ $\phantom{-}5e^{5} + 7e^{4} - 31e^{3} - 28e^{2} + 25e$
53 $[53, 53, 26w - 151]$ $-6e^{5} - 11e^{4} + 35e^{3} + 50e^{2} - 21e - 22$
61 $[61, 61, -14w + 81]$ $-2e^{3} - 3e^{2} + 8e + 3$
61 $[61, 61, -14w - 67]$ $\phantom{-}9e^{5} + 15e^{4} - 55e^{3} - 69e^{2} + 40e + 23$
83 $[83, 83, 2w - 15]$ $\phantom{-}4e^{5} + 7e^{4} - 24e^{3} - 31e^{2} + 16e$
83 $[83, 83, -2w - 13]$ $-2e^{5} - 2e^{4} + 13e^{3} + 5e^{2} - 12e - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, 3]$ $-1$