Properties

Base field \(\Q(\sqrt{101}) \)
Weight [2, 2]
Level norm 25
Level $[25,25,-w + 1]$
Label 2.2.101.1-25.3-c
Dimension 4
CM no
Base change no

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Base field \(\Q(\sqrt{101}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 25\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[25,25,-w + 1]$
Label 2.2.101.1-25.3-c
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 30

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut +\mathstrut 3x^{3} \) \(\mathstrut -\mathstrut 9x^{2} \) \(\mathstrut -\mathstrut 27x \) \(\mathstrut -\mathstrut 8\)

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Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}e$
5 $[5, 5, -w + 5]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{2}e^{2} - \frac{7}{4}e - 3$
5 $[5, 5, -w - 4]$ $\phantom{-}0$
9 $[9, 3, 3]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 6$
13 $[13, 13, w + 3]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 4e + 3$
13 $[13, 13, w - 4]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - 4e - 3$
17 $[17, 17, w + 6]$ $\phantom{-}\frac{3}{4}e^{3} + e^{2} - \frac{31}{4}e - 7$
17 $[17, 17, -w + 7]$ $-\frac{3}{4}e^{3} - e^{2} + \frac{31}{4}e + 7$
19 $[19, 19, w + 2]$ $\phantom{-}e^{2} - 7$
19 $[19, 19, w - 3]$ $\phantom{-}e^{2} - 7$
23 $[23, 23, w + 1]$ $-\frac{1}{2}e^{3} - e^{2} + \frac{13}{2}e + 9$
23 $[23, 23, -w + 2]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - \frac{13}{2}e - 9$
31 $[31, 31, -w - 7]$ $-e + 1$
31 $[31, 31, w - 8]$ $-e + 1$
37 $[37, 37, 2w - 9]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{13}{4}e - 4$
37 $[37, 37, 2w + 7]$ $-\frac{1}{4}e^{3} + \frac{13}{4}e + 4$
43 $[43, 43, 4w + 17]$ $-2e - 4$
43 $[43, 43, 4w - 21]$ $\phantom{-}2e + 4$
47 $[47, 47, -w - 8]$ $\phantom{-}e^{3} + e^{2} - 9e - 11$
47 $[47, 47, w - 9]$ $-e^{3} - e^{2} + 9e + 11$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5,5,w + 4]$ $1$