Properties

Label 4.4.18736.1-7.1-b
Base field 4.4.18736.1
Weight $[2, 2, 2, 2]$
Level norm $7$
Level $[7, 7, w - 2]$
Dimension $10$
CM no
Base change no

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Base field 4.4.18736.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[7, 7, w - 2]$
Dimension: $10$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{10} - 18x^{8} + 92x^{6} - 132x^{4} + 60x^{2} - 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w - 1]$ $\phantom{-}e$
4 $[4, 2, -w^{3} + 2w^{2} + 4w - 3]$ $-\frac{3}{4}e^{9} + \frac{53}{4}e^{7} - \frac{129}{2}e^{5} + \frac{153}{2}e^{3} - 17e$
5 $[5, 5, w]$ $\phantom{-}\frac{1}{4}e^{9} - \frac{9}{2}e^{7} + 23e^{5} - 33e^{3} + 14e$
7 $[7, 7, w - 2]$ $-1$
11 $[11, 11, w^{2} - 2w - 4]$ $-\frac{3}{4}e^{8} + 13e^{6} - \frac{121}{2}e^{4} + 61e^{2} - 10$
23 $[23, 23, -w^{2} + 2w + 1]$ $\phantom{-}\frac{3}{4}e^{9} - \frac{27}{2}e^{7} + 69e^{5} - 98e^{3} + 37e$
23 $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ $-\frac{1}{4}e^{9} + \frac{9}{2}e^{7} - 23e^{5} + 32e^{3} - 5e$
27 $[27, 3, -w^{3} + w^{2} + 6w + 2]$ $\phantom{-}\frac{11}{4}e^{9} - \frac{97}{2}e^{7} + \frac{471}{2}e^{5} - 280e^{3} + 74e$
31 $[31, 31, -w^{3} + 3w^{2} + w - 1]$ $\phantom{-}\frac{3}{4}e^{8} - \frac{27}{2}e^{6} + \frac{137}{2}e^{4} - 92e^{2} + 28$
31 $[31, 31, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}2e^{9} - \frac{71}{2}e^{7} + 175e^{5} - 219e^{3} + 63e$
37 $[37, 37, w^{2} - 2w - 6]$ $-\frac{3}{4}e^{8} + \frac{27}{2}e^{6} - \frac{137}{2}e^{4} + 92e^{2} - 24$
37 $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ $\phantom{-}3e^{9} - 53e^{7} + \frac{517}{2}e^{5} - 312e^{3} + 83e$
43 $[43, 43, w^{2} - 3w - 2]$ $-\frac{9}{4}e^{9} + 40e^{7} - 198e^{5} + 251e^{3} - 73e$
61 $[61, 61, -w^{3} + 2w^{2} + 2w - 2]$ $\phantom{-}\frac{5}{4}e^{9} - 22e^{7} + 106e^{5} - 121e^{3} + 27e$
73 $[73, 73, w^{3} - 3w^{2} - 2w + 3]$ $\phantom{-}\frac{3}{2}e^{9} - 26e^{7} + 121e^{5} - 122e^{3} + 22e$
83 $[83, 83, -w - 3]$ $\phantom{-}2e^{2} - 10$
89 $[89, 89, -w^{3} + 3w^{2} + 2w - 2]$ $\phantom{-}\frac{1}{2}e^{9} - 8e^{7} + 29e^{5} + 10e^{3} - 36e$
89 $[89, 89, 2w - 1]$ $\phantom{-}\frac{3}{4}e^{9} - \frac{27}{2}e^{7} + 69e^{5} - 98e^{3} + 39e$
101 $[101, 101, w^{3} - 4w^{2} + w + 7]$ $\phantom{-}2e^{8} - 35e^{6} + 167e^{4} - 186e^{2} + 42$
101 $[101, 101, 2w^{2} - 3w - 3]$ $\phantom{-}\frac{23}{4}e^{9} - \frac{203}{2}e^{7} + 494e^{5} - 591e^{3} + 152e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, w - 2]$ $1$