# Properties

 Label 4.4.12725.1-11.1-b Base field 4.4.12725.1 Weight $[2, 2, 2, 2]$ Level norm $11$ Level $[11, 11, -w - 1]$ Dimension $7$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.12725.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 10x^{2} + 11x + 29$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[11, 11, -w - 1]$ Dimension: $7$ CM: no Base change: no Newspace dimension: $10$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{7} - 12x^{6} + 36x^{5} + 41x^{4} - 332x^{3} + 459x^{2} - 201x + 27$$
Norm Prime Eigenvalue
11 $[11, 11, -w - 1]$ $-1$
11 $[11, 11, w^{2} - 5]$ $\phantom{-}e$
11 $[11, 11, -w^{2} + 2w + 4]$ $\phantom{-}\frac{1775}{6621}e^{6} - \frac{6549}{2207}e^{5} + \frac{15507}{2207}e^{4} + \frac{107881}{6621}e^{3} - \frac{481963}{6621}e^{2} + \frac{143671}{2207}e - \frac{21540}{2207}$
11 $[11, 11, w - 2]$ $-\frac{687}{2207}e^{6} + \frac{8068}{2207}e^{5} - \frac{22437}{2207}e^{4} - \frac{35698}{2207}e^{3} + \frac{219231}{2207}e^{2} - \frac{242843}{2207}e + \frac{56692}{2207}$
16 $[16, 2, 2]$ $-\frac{1879}{6621}e^{6} + \frac{7302}{2207}e^{5} - \frac{20234}{2207}e^{4} - \frac{93149}{6621}e^{3} + \frac{591008}{6621}e^{2} - \frac{234106}{2207}e + \frac{57797}{2207}$
19 $[19, 19, w^{2} - 2w - 5]$ $\phantom{-}\frac{722}{6621}e^{6} - \frac{3063}{2207}e^{5} + \frac{9855}{2207}e^{4} + \frac{35239}{6621}e^{3} - \frac{285787}{6621}e^{2} + \frac{105575}{2207}e - \frac{9489}{2207}$
19 $[19, 19, -w^{2} + 6]$ $\phantom{-}\frac{776}{6621}e^{6} - \frac{3072}{2207}e^{5} + \frac{9296}{2207}e^{4} + \frac{28099}{6621}e^{3} - \frac{260026}{6621}e^{2} + \frac{125411}{2207}e - \frac{34384}{2207}$
25 $[25, 5, -2w^{2} + 2w + 11]$ $\phantom{-}\frac{3079}{6621}e^{6} - \frac{11916}{2207}e^{5} + \frac{32334}{2207}e^{4} + \frac{162539}{6621}e^{3} - \frac{952838}{6621}e^{2} + \frac{350477}{2207}e - \frac{87715}{2207}$
29 $[29, 29, w]$ $-\frac{2359}{6621}e^{6} + \frac{9589}{2207}e^{5} - \frac{29488}{2207}e^{4} - \frac{101042}{6621}e^{3} + \frac{841676}{6621}e^{2} - \frac{361872}{2207}e + \frac{97131}{2207}$
29 $[29, 29, 2w^{2} - w - 10]$ $\phantom{-}\frac{3497}{6621}e^{6} - \frac{13457}{2207}e^{5} + \frac{36181}{2207}e^{4} + \frac{183289}{6621}e^{3} - \frac{1067068}{6621}e^{2} + \frac{401029}{2207}e - \frac{103779}{2207}$
29 $[29, 29, -2w^{2} + 3w + 9]$ $-\frac{739}{6621}e^{6} + \frac{2698}{2207}e^{5} - \frac{6532}{2207}e^{4} - \frac{37160}{6621}e^{3} + \frac{190991}{6621}e^{2} - \frac{80186}{2207}e + \frac{34451}{2207}$
29 $[29, 29, w - 1]$ $\phantom{-}\frac{1147}{6621}e^{6} - \frac{4973}{2207}e^{5} + \frac{17267}{2207}e^{4} + \frac{36917}{6621}e^{3} - \frac{471593}{6621}e^{2} + \frac{227851}{2207}e - \frac{66340}{2207}$
31 $[31, 31, w^{3} - 6w - 6]$ $\phantom{-}\frac{327}{2207}e^{6} - \frac{3474}{2207}e^{5} + \frac{7133}{2207}e^{4} + \frac{21502}{2207}e^{3} - \frac{75370}{2207}e^{2} + \frac{60202}{2207}e - \frac{20055}{2207}$
31 $[31, 31, -w^{3} + 3w^{2} + 3w - 11]$ $\phantom{-}\frac{436}{6621}e^{6} - \frac{1544}{2207}e^{5} + \frac{2925}{2207}e^{4} + \frac{36026}{6621}e^{3} - \frac{110057}{6621}e^{2} + \frac{4196}{2207}e + \frac{25663}{2207}$
41 $[41, 41, w^{3} - 4w^{2} - 2w + 16]$ $\phantom{-}\frac{1103}{6621}e^{6} - \frac{4230}{2207}e^{5} + \frac{10938}{2207}e^{4} + \frac{65050}{6621}e^{3} - \frac{330982}{6621}e^{2} + \frac{108695}{2207}e - \frac{14585}{2207}$
41 $[41, 41, w^{3} - 5w^{2} - 2w + 24]$ $-\frac{1014}{2207}e^{6} + \frac{11542}{2207}e^{5} - \frac{29570}{2207}e^{4} - \frac{57200}{2207}e^{3} + \frac{294601}{2207}e^{2} - \frac{305252}{2207}e + \frac{74540}{2207}$
59 $[59, 59, w^{3} - w^{2} - 5w - 2]$ $-\frac{6686}{6621}e^{6} + \frac{26127}{2207}e^{5} - \frac{72199}{2207}e^{4} - \frac{351637}{6621}e^{3} + \frac{2116525}{6621}e^{2} - \frac{773521}{2207}e + \frac{185151}{2207}$
59 $[59, 59, 2w^{2} - w - 13]$ $\phantom{-}\frac{10544}{6621}e^{6} - \frac{40012}{2207}e^{5} + \frac{103376}{2207}e^{4} + \frac{582340}{6621}e^{3} - \frac{3098062}{6621}e^{2} + \frac{1084986}{2207}e - \frac{250638}{2207}$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $\phantom{-}\frac{3644}{6621}e^{6} - \frac{14585}{2207}e^{5} + \frac{42629}{2207}e^{4} + \frac{180037}{6621}e^{3} - \frac{1239343}{6621}e^{2} + \frac{477097}{2207}e - \frac{97369}{2207}$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}\frac{1627}{6621}e^{6} - \frac{7260}{2207}e^{5} + \frac{26521}{2207}e^{4} + \frac{44810}{6621}e^{3} - \frac{722261}{6621}e^{2} + \frac{353410}{2207}e - \frac{92432}{2207}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11, 11, -w - 1]$ $1$