# Properties

 Label 4.4.18097.1-16.2-a Base field 4.4.18097.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 4, -w^{3} + 6w]$ Dimension $12$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.18097.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 4, -w^{3} + 6w]$ Dimension: $12$ CM: no Base change: no Newspace dimension: $28$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{12} - 19x^{10} + 122x^{8} - 339x^{6} + 427x^{4} - 212x^{2} + 16$$
Norm Prime Eigenvalue
3 $[3, 3, -w + 1]$ $\phantom{-}e$
4 $[4, 2, w]$ $\phantom{-}0$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ $-\frac{3}{4}e^{11} + \frac{107}{8}e^{9} - 76e^{7} + \frac{335}{2}e^{5} - \frac{1087}{8}e^{3} + 23e$
7 $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$ $-\frac{21}{8}e^{10} + \frac{93}{2}e^{8} - \frac{1041}{4}e^{6} + \frac{4417}{8}e^{4} - 399e^{2} + 30$
13 $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ $\phantom{-}\frac{43}{8}e^{10} - 95e^{8} + \frac{2119}{4}e^{6} - \frac{8951}{8}e^{4} + \frac{1615}{2}e^{2} - 64$
17 $[17, 17, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w]$ $\phantom{-}e^{11} - 18e^{9} + 104e^{7} - 235e^{5} + 193e^{3} - 29e$
27 $[27, 3, -w^{3} + 7w + 1]$ $-\frac{3}{8}e^{11} + \frac{13}{2}e^{9} - \frac{139}{4}e^{7} + \frac{527}{8}e^{5} - 29e^{3} - 19e$
31 $[31, 31, w + 3]$ $-\frac{27}{4}e^{10} + \frac{239}{2}e^{8} - \frac{1337}{2}e^{6} + \frac{5683}{4}e^{4} - \frac{2083}{2}e^{2} + 92$
31 $[31, 31, -w^{2} + 5]$ $\phantom{-}\frac{9}{4}e^{11} - \frac{159}{4}e^{9} + \frac{443}{2}e^{7} - \frac{1871}{4}e^{5} + \frac{1363}{4}e^{3} - 31e$
37 $[37, 37, w^{2} - 3]$ $\phantom{-}\frac{11}{2}e^{11} - \frac{389}{4}e^{9} + 543e^{7} - 1152e^{5} + \frac{3385}{4}e^{3} - 78e$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{3}{2}w - 2]$ $-\frac{19}{4}e^{11} + \frac{335}{4}e^{9} - \frac{929}{2}e^{7} + \frac{3873}{4}e^{5} - \frac{2691}{4}e^{3} + 33e$
47 $[47, 47, w^{3} - 5w - 3]$ $\phantom{-}\frac{11}{8}e^{11} - 24e^{9} + \frac{523}{4}e^{7} - \frac{2127}{8}e^{5} + \frac{375}{2}e^{3} - 25e$
53 $[53, 53, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w]$ $-\frac{49}{8}e^{11} + \frac{431}{4}e^{9} - \frac{2381}{4}e^{7} + \frac{9865}{8}e^{5} - \frac{3397}{4}e^{3} + 40e$
61 $[61, 61, w^{3} - w^{2} - 5w + 3]$ $-\frac{57}{8}e^{10} + \frac{251}{2}e^{8} - \frac{2781}{4}e^{6} + \frac{11605}{8}e^{4} - 1025e^{2} + 72$
83 $[83, 83, w^{3} + w^{2} - 6w - 7]$ $\phantom{-}\frac{3}{8}e^{11} - \frac{27}{4}e^{9} + \frac{155}{4}e^{7} - \frac{675}{8}e^{5} + \frac{229}{4}e^{3} + 7e$
83 $[83, 83, -w^{3} + 5w + 1]$ $\phantom{-}\frac{7}{4}e^{10} - \frac{63}{2}e^{8} + \frac{363}{2}e^{6} - \frac{1619}{4}e^{4} + \frac{641}{2}e^{2} - 44$
83 $[83, 83, 2w - 1]$ $-\frac{1}{4}e^{11} + \frac{17}{4}e^{9} - \frac{43}{2}e^{7} + \frac{131}{4}e^{5} + \frac{43}{4}e^{3} - 43e$
83 $[83, 83, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 2]$ $\phantom{-}\frac{61}{8}e^{10} - 135e^{8} + \frac{3021}{4}e^{6} - \frac{12833}{8}e^{4} + \frac{2335}{2}e^{2} - 98$
89 $[89, 89, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 2]$ $-\frac{1}{2}e^{8} + 8e^{6} - 37e^{4} + \frac{109}{2}e^{2} - 18$
89 $[89, 89, w^{3} - 5w + 5]$ $\phantom{-}\frac{5}{4}e^{10} - \frac{45}{2}e^{8} + \frac{259}{2}e^{6} - \frac{1145}{4}e^{4} + \frac{425}{2}e^{2} - 18$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, w]$ $-1$