# Properties

 Label 4.4.11661.1-23.1-h Base field 4.4.11661.1 Weight $[2, 2, 2, 2]$ Level norm $23$ Level $[23, 23, -w^{3} + 4w + 1]$ Dimension $12$ CM no Base change no

# Related objects

• L-function not available

# Learn more about

## Base field 4.4.11661.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[23, 23, -w^{3} + 4w + 1]$ Dimension: $12$ CM: no Base change: no Newspace dimension: $30$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{12} - 20x^{10} + 146x^{8} - 467x^{6} + 589x^{4} - 128x^{2} + 4$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w - 2]$ $\phantom{-}\frac{21}{146}e^{11} - \frac{198}{73}e^{9} + \frac{1338}{73}e^{7} - \frac{7729}{146}e^{5} + \frac{8479}{146}e^{3} - \frac{639}{73}e$
3 $[3, 3, w - 1]$ $-\frac{7}{146}e^{11} + \frac{66}{73}e^{9} - \frac{446}{73}e^{7} + \frac{2625}{146}e^{5} - \frac{3313}{146}e^{3} + \frac{724}{73}e$
16 $[16, 2, 2]$ $-\frac{11}{73}e^{10} + \frac{197}{73}e^{8} - \frac{1214}{73}e^{6} + \frac{2957}{73}e^{4} - \frac{2380}{73}e^{2} + \frac{75}{73}$
23 $[23, 23, -w^{3} + 4w + 1]$ $\phantom{-}1$
25 $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ $-\frac{99}{584}e^{11} + \frac{923}{292}e^{9} - \frac{6193}{292}e^{7} + \frac{35957}{584}e^{5} - \frac{41349}{584}e^{3} + \frac{4827}{292}e$
25 $[25, 5, w^{3} - w^{2} - 3w + 1]$ $-\frac{209}{584}e^{11} + \frac{1981}{292}e^{9} - \frac{13431}{292}e^{7} + \frac{77207}{584}e^{5} - \frac{81063}{584}e^{3} + \frac{2209}{292}e$
29 $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ $-\frac{55}{584}e^{11} + \frac{675}{292}e^{9} - \frac{6101}{292}e^{7} + \frac{48073}{584}e^{5} - \frac{71833}{584}e^{3} + \frac{6867}{292}e$
29 $[29, 29, w^{3} - w^{2} - 5w + 1]$ $-\frac{17}{584}e^{11} + \frac{129}{292}e^{9} - \frac{447}{292}e^{7} - \frac{2385}{584}e^{5} + \frac{14897}{584}e^{3} - \frac{7179}{292}e$
43 $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}\frac{15}{292}e^{10} - \frac{131}{146}e^{8} + \frac{841}{146}e^{6} - \frac{5041}{292}e^{4} + \frac{6849}{292}e^{2} - \frac{1395}{146}$
43 $[43, 43, w^{3} - w^{2} - 4w + 2]$ $-\frac{15}{292}e^{10} + \frac{131}{146}e^{8} - \frac{841}{146}e^{6} + \frac{5041}{292}e^{4} - \frac{6849}{292}e^{2} + \frac{227}{146}$
61 $[61, 61, -w^{2} + 2w + 4]$ $\phantom{-}\frac{13}{584}e^{11} - \frac{133}{292}e^{9} + \frac{943}{292}e^{7} - \frac{5459}{584}e^{5} + \frac{7571}{584}e^{3} - \frac{5005}{292}e$
61 $[61, 61, w^{2} - 5]$ $\phantom{-}\frac{7}{8}e^{11} - \frac{71}{4}e^{9} + \frac{525}{4}e^{7} - \frac{3377}{8}e^{5} + \frac{4153}{8}e^{3} - \frac{303}{4}e$
79 $[79, 79, 3w^{3} - 7w^{2} - 8w + 16]$ $\phantom{-}\frac{295}{292}e^{11} - \frac{3063}{146}e^{9} + \frac{23353}{146}e^{7} - \frac{156177}{292}e^{5} + \frac{201565}{292}e^{3} - \frac{16193}{146}e$
79 $[79, 79, -w^{3} + w^{2} + 6w - 4]$ $-\frac{89}{292}e^{11} + \frac{933}{146}e^{9} - \frac{7287}{146}e^{7} + \frac{51187}{292}e^{5} - \frac{72699}{292}e^{3} + \frac{9007}{146}e$
101 $[101, 101, -w^{3} + 3w^{2} + w - 7]$ $\phantom{-}\frac{49}{584}e^{11} - \frac{389}{292}e^{9} + \frac{2027}{292}e^{7} - \frac{7863}{584}e^{5} + \frac{5087}{584}e^{3} - \frac{177}{292}e$
101 $[101, 101, w^{3} - 4w - 4]$ $-\frac{293}{584}e^{11} + \frac{3065}{292}e^{9} - \frac{23455}{292}e^{7} + \frac{156595}{584}e^{5} - \frac{200827}{584}e^{3} + \frac{16445}{292}e$
103 $[103, 103, 2w^{3} - w^{2} - 8w - 1]$ $\phantom{-}\frac{1}{292}e^{10} + \frac{147}{146}e^{8} - \frac{2387}{146}e^{6} + \frac{24445}{292}e^{4} - \frac{41533}{292}e^{2} + \frac{2535}{146}$
103 $[103, 103, 2w^{3} - 5w^{2} - 4w + 8]$ $-\frac{105}{292}e^{10} + \frac{771}{146}e^{8} - \frac{3113}{146}e^{6} + \frac{831}{292}e^{4} + \frac{23597}{292}e^{2} - \frac{2207}{146}$
107 $[107, 107, 2w^{2} - 3w - 4]$ $-\frac{109}{292}e^{10} + \frac{913}{146}e^{8} - \frac{5099}{146}e^{6} + \frac{20727}{292}e^{4} - \frac{9707}{292}e^{2} + \frac{501}{146}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$23$ $[23, 23, -w^{3} + 4w + 1]$ $-1$