Properties

Base field \(\Q(\sqrt{34}) \)
Weight [2, 2]
Level norm 3
Level $[3, 3, w + 1]$
Label 2.2.136.1-3.1-c
Dimension 4
CM no
Base change no

Related objects

Downloads

Learn more about

Base field \(\Q(\sqrt{34}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 34\); narrow class number \(4\) and class number \(2\).

Form

Weight [2, 2]
Level $[3, 3, w + 1]$
Label 2.2.136.1-3.1-c
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 8

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut +\mathstrut 7x^{2} \) \(\mathstrut +\mathstrut 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 6]$ $\phantom{-}\frac{1}{3}e^{2} + \frac{5}{3}$
3 $[3, 3, w + 1]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{8}{3}e$
3 $[3, 3, w + 2]$ $\phantom{-}e$
5 $[5, 5, w + 2]$ $-\frac{4}{3}e^{3} - \frac{23}{3}e$
5 $[5, 5, w + 3]$ $-\frac{5}{3}e^{3} - \frac{34}{3}e$
11 $[11, 11, w + 1]$ $-\frac{4}{3}e^{3} - \frac{29}{3}e$
11 $[11, 11, w + 10]$ $\phantom{-}\frac{4}{3}e^{3} + \frac{29}{3}e$
17 $[17, 17, -3w + 17]$ $\phantom{-}\frac{2}{3}e^{2} + \frac{1}{3}$
29 $[29, 29, w + 11]$ $-\frac{11}{3}e^{3} - \frac{79}{3}e$
29 $[29, 29, w + 18]$ $\phantom{-}\frac{7}{3}e^{3} + \frac{44}{3}e$
37 $[37, 37, w + 16]$ $\phantom{-}e^{3} + 4e$
37 $[37, 37, w + 21]$ $\phantom{-}2e^{3} + 15e$
47 $[47, 47, -w - 9]$ $\phantom{-}\frac{4}{3}e^{2} + \frac{38}{3}$
47 $[47, 47, w - 9]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{10}{3}$
49 $[49, 7, -7]$ $\phantom{-}e^{2} - 4$
61 $[61, 61, w + 20]$ $-e^{3} - e$
61 $[61, 61, w + 41]$ $-\frac{11}{3}e^{3} - \frac{76}{3}e$
89 $[89, 89, 2w - 15]$ $-\frac{4}{3}e^{2} + \frac{1}{3}$
89 $[89, 89, -2w - 15]$ $\phantom{-}\frac{4}{3}e^{2} - \frac{16}{3}$
103 $[103, 103, -14w + 81]$ $\phantom{-}\frac{5}{3}e^{2} + \frac{7}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $-\frac{1}{3}e^{3} - \frac{8}{3}e$