Properties

Base field \(\Q(\sqrt{113}) \)
Weight [2, 2]
Level norm 4
Level $[4,4,5w - 29]$
Label 2.2.113.1-4.3-a
Dimension 3
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 $[4,4,5w - 29]$
Label 2.2.113.1-4.3-a
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 3

Hecke eigenvalues ($q$-expansion)

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

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Norm Prime Eigenvalue
2 $[2, 2, -w + 6]$ $\phantom{-}e$
2 $[2, 2, w + 5]$ $\phantom{-}0$
7 $[7, 7, 6w - 35]$ $-e^{2} - e + 2$
7 $[7, 7, -6w - 29]$ $\phantom{-}e^{2} + e - 4$
9 $[9, 3, 3]$ $-e^{2} - e + 1$
11 $[11, 11, 4w + 19]$ $\phantom{-}e^{2} + 2e$
11 $[11, 11, 4w - 23]$ $\phantom{-}e^{2} - 6$
13 $[13, 13, -2w + 11]$ $-e^{2} - 4e + 2$
13 $[13, 13, 2w + 9]$ $-e^{2} + 2$
25 $[25, 5, -5]$ $\phantom{-}2e^{2} + 2e - 7$
31 $[31, 31, 2w - 13]$ $\phantom{-}e^{2} + e - 7$
31 $[31, 31, -2w - 11]$ $-e^{2} + e - 1$
41 $[41, 41, -8w - 39]$ $\phantom{-}3e + 3$
41 $[41, 41, 8w - 47]$ $-e + 3$
53 $[53, 53, -26w - 125]$ $-2e^{2} - e + 3$
53 $[53, 53, 26w - 151]$ $\phantom{-}2e^{2} - e - 9$
61 $[61, 61, -14w + 81]$ $-e^{2} - 2e - 7$
61 $[61, 61, -14w - 67]$ $-e^{2} - 6e + 5$
83 $[83, 83, 2w - 15]$ $-4e^{2} - 5e + 6$
83 $[83, 83, -2w - 13]$ $\phantom{-}2e^{2} + 7e - 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,w + 5]$ $-1$