Properties

Base field \(\Q(\sqrt{113}) \)
Weight [2, 2]
Level norm 1
Level $[1, 1, 1]$
Label 2.2.113.1-1.1-a
Dimension 4
CM no
Base change yes

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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 $[1, 1, 1]$
Label 2.2.113.1-1.1-a
Dimension 4
Is CM no
Is base change yes
Parent newspace dimension 4

Hecke eigenvalues ($q$-expansion)

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

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Norm Prime Eigenvalue
2 $[2, 2, -w + 6]$ $\phantom{-}e$
2 $[2, 2, w + 5]$ $\phantom{-}e$
7 $[7, 7, 6w - 35]$ $-e^{2} - e + 2$
7 $[7, 7, -6w - 29]$ $-e^{2} - e + 2$
9 $[9, 3, 3]$ $\phantom{-}e^{3} - e^{2} - 4e + 4$
11 $[11, 11, 4w + 19]$ $\phantom{-}e^{3} - e^{2} - 3e + 3$
11 $[11, 11, 4w - 23]$ $\phantom{-}e^{3} - e^{2} - 3e + 3$
13 $[13, 13, -2w + 11]$ $-e^{3} + e^{2} + 5e - 1$
13 $[13, 13, 2w + 9]$ $-e^{3} + e^{2} + 5e - 1$
25 $[25, 5, -5]$ $-3e^{3} + 11e + 2$
31 $[31, 31, 2w - 13]$ $\phantom{-}e^{3} + e^{2} - 6e - 4$
31 $[31, 31, -2w - 11]$ $\phantom{-}e^{3} + e^{2} - 6e - 4$
41 $[41, 41, -8w - 39]$ $\phantom{-}2e^{3} + 2e^{2} - 9e - 3$
41 $[41, 41, 8w - 47]$ $\phantom{-}2e^{3} + 2e^{2} - 9e - 3$
53 $[53, 53, -26w - 125]$ $-4e^{3} + 17e + 3$
53 $[53, 53, 26w - 151]$ $-4e^{3} + 17e + 3$
61 $[61, 61, -14w + 81]$ $-e^{2} - 2e + 5$
61 $[61, 61, -14w - 67]$ $-e^{2} - 2e + 5$
83 $[83, 83, 2w - 15]$ $-e^{3} + 6e^{2} + 6e - 15$
83 $[83, 83, -2w - 13]$ $-e^{3} + 6e^{2} + 6e - 15$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).