Properties

Base field 4.4.8768.1
Weight [2, 2, 2, 2]
Level norm 28
Level $[28, 14, -w^{3} + 3w^{2} + w - 4]$
Label 4.4.8768.1-28.2-c
Dimension 3
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 4.4.8768.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 6x + 7\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[28, 14, -w^{3} + 3w^{2} + w - 4]$
Label 4.4.8768.1-28.2-c
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 14

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} \) \(\mathstrut +\mathstrut 7x^{2} \) \(\mathstrut +\mathstrut x \) \(\mathstrut -\mathstrut 46\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $-1$
7 $[7, 7, w]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 2w + 1]$ $\phantom{-}1$
7 $[7, 7, w^{2} - 2]$ $\phantom{-}2e^{2} + 5e - 21$
7 $[7, 7, w - 1]$ $-2e^{2} - 5e + 21$
23 $[23, 23, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}4e^{2} + 8e - 44$
23 $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ $-6e^{2} - 15e + 58$
31 $[31, 31, w^{2} - 5]$ $\phantom{-}5e^{2} + 13e - 49$
31 $[31, 31, -w^{2} + 2w + 4]$ $\phantom{-}3e^{2} + 6e - 36$
41 $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ $-9e^{2} - 21e + 93$
41 $[41, 41, w^{3} - w^{2} - 3w - 3]$ $\phantom{-}6e^{2} + 13e - 64$
47 $[47, 47, w^{2} - 2w - 5]$ $\phantom{-}8e^{2} + 19e - 82$
47 $[47, 47, w^{2} - 6]$ $-2e^{2} - 5e + 12$
71 $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ $\phantom{-}e^{2} + 5e - 11$
71 $[71, 71, -w^{3} + w^{2} + 4w - 3]$ $-3e^{2} - 7e + 31$
79 $[79, 79, -w - 3]$ $\phantom{-}e^{2} + 2e - 16$
79 $[79, 79, w - 4]$ $-4e^{2} - 9e + 39$
81 $[81, 3, -3]$ $-13e^{2} - 33e + 125$
89 $[89, 89, w^{2} - 3w - 2]$ $\phantom{-}9e^{2} + 20e - 99$
89 $[89, 89, w^{2} + w - 4]$ $-3e^{2} - 8e + 32$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $1$
7 $[7, 7, -w^{2} + 2w + 1]$ $-1$