Properties

Base field 4.4.16997.1
Weight [2, 2, 2, 2]
Level norm 25
Level $[25, 25, -w^{3} + 5w + 3]$
Label 4.4.16997.1-25.3-i
Dimension 9
CM no
Base change no

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Base field 4.4.16997.1

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

Form

Weight [2, 2, 2, 2]
Level $[25, 25, -w^{3} + 5w + 3]$
Label 4.4.16997.1-25.3-i
Dimension 9
Is CM no
Is base change no
Parent newspace dimension 39

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{9} - 29x^{7} - 18x^{6} + 239x^{5} + 275x^{4} - 441x^{3} - 669x^{2} - 27x + 144\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w]$ $\phantom{-}e$
5 $[5, 5, -w^{2} + w + 2]$ $\phantom{-}0$
7 $[7, 7, -w^{2} + 2]$ $-\frac{139}{1545}e^{8} + \frac{244}{1545}e^{7} + \frac{3659}{1545}e^{6} - \frac{1348}{515}e^{5} - \frac{9193}{515}e^{4} + \frac{4132}{515}e^{3} + \frac{10151}{309}e^{2} - \frac{1039}{515}e - \frac{747}{103}$
13 $[13, 13, -w^{2} + 3]$ $-\frac{7}{103}e^{8} + \frac{128}{1545}e^{7} + \frac{2887}{1545}e^{6} - \frac{1598}{1545}e^{5} - \frac{23042}{1545}e^{4} - \frac{1852}{1545}e^{3} + \frac{46898}{1545}e^{2} + \frac{1411}{103}e - \frac{4482}{515}$
13 $[13, 13, w^{2} - w - 4]$ $\phantom{-}\frac{139}{1545}e^{8} - \frac{244}{1545}e^{7} - \frac{3659}{1545}e^{6} + \frac{1348}{515}e^{5} + \frac{9193}{515}e^{4} - \frac{4132}{515}e^{3} - \frac{10151}{309}e^{2} + \frac{1554}{515}e + \frac{850}{103}$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{1545}e^{8} + \frac{13}{515}e^{7} - \frac{52}{515}e^{6} - \frac{283}{515}e^{5} + \frac{922}{515}e^{4} + \frac{4531}{1545}e^{3} - \frac{2671}{309}e^{2} - \frac{1004}{515}e + \frac{819}{103}$
19 $[19, 19, -w^{2} + w + 1]$ $\phantom{-}\frac{23}{1545}e^{8} - \frac{2}{103}e^{7} - \frac{601}{1545}e^{6} + \frac{91}{309}e^{5} + \frac{1327}{515}e^{4} - \frac{1259}{1545}e^{3} - \frac{637}{1545}e^{2} + \frac{1113}{515}e - \frac{3562}{515}$
23 $[23, 23, -w^{3} + 4w + 2]$ $-\frac{118}{515}e^{8} + \frac{511}{1545}e^{7} + \frac{3164}{515}e^{6} - \frac{7321}{1545}e^{5} - \frac{73382}{1545}e^{4} + \frac{8903}{1545}e^{3} + \frac{47164}{515}e^{2} + \frac{9851}{515}e - \frac{11853}{515}$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}\frac{106}{309}e^{8} - \frac{217}{515}e^{7} - \frac{14494}{1545}e^{6} + \frac{8071}{1545}e^{5} + \frac{114929}{1545}e^{4} + \frac{7504}{1545}e^{3} - \frac{229886}{1545}e^{2} - \frac{5175}{103}e + \frac{20019}{515}$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}\frac{118}{515}e^{8} - \frac{511}{1545}e^{7} - \frac{3164}{515}e^{6} + \frac{7321}{1545}e^{5} + \frac{73382}{1545}e^{4} - \frac{8903}{1545}e^{3} - \frac{47164}{515}e^{2} - \frac{10366}{515}e + \frac{11853}{515}$
29 $[29, 29, -w + 3]$ $\phantom{-}\frac{91}{309}e^{8} - \frac{589}{1545}e^{7} - \frac{12476}{1545}e^{6} + \frac{2663}{515}e^{5} + \frac{33157}{515}e^{4} - \frac{3854}{1545}e^{3} - \frac{67753}{515}e^{2} - \frac{2887}{103}e + \frac{21276}{515}$
31 $[31, 31, -w^{3} + w^{2} + 5w - 2]$ $\phantom{-}\frac{112}{309}e^{8} - \frac{239}{515}e^{7} - \frac{5121}{515}e^{6} + \frac{9587}{1545}e^{5} + \frac{122513}{1545}e^{4} - \frac{2002}{1545}e^{3} - \frac{250157}{1545}e^{2} - \frac{4195}{103}e + \frac{25758}{515}$
37 $[37, 37, w^{3} - 4w - 1]$ $\phantom{-}\frac{139}{1545}e^{8} - \frac{244}{1545}e^{7} - \frac{3659}{1545}e^{6} + \frac{1348}{515}e^{5} + \frac{9193}{515}e^{4} - \frac{4132}{515}e^{3} - \frac{9842}{309}e^{2} + \frac{1039}{515}e + \frac{232}{103}$
37 $[37, 37, w^{3} - 3w + 1]$ $\phantom{-}\frac{49}{309}e^{8} - \frac{111}{515}e^{7} - \frac{2234}{515}e^{6} + \frac{4793}{1545}e^{5} + \frac{53387}{1545}e^{4} - \frac{6013}{1545}e^{3} - \frac{109463}{1545}e^{2} - \frac{1507}{103}e + \frac{8707}{515}$
53 $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ $-\frac{797}{1545}e^{8} + \frac{351}{515}e^{7} + \frac{21641}{1545}e^{6} - \frac{14168}{1545}e^{5} - \frac{169531}{1545}e^{4} + \frac{1433}{515}e^{3} + \frac{109907}{515}e^{2} + \frac{30263}{515}e - \frac{25704}{515}$
59 $[59, 59, w^{2} + w - 4]$ $-\frac{231}{515}e^{8} + \frac{886}{1545}e^{7} + \frac{3782}{309}e^{6} - \frac{3907}{515}e^{5} - \frac{29851}{309}e^{4} + \frac{5}{103}e^{3} + \frac{98726}{515}e^{2} + \frac{30907}{515}e - \frac{25317}{515}$
61 $[61, 61, -2w^{2} + w + 8]$ $-\frac{316}{1545}e^{8} + \frac{23}{103}e^{7} + \frac{2939}{515}e^{6} - \frac{263}{103}e^{5} - \frac{23964}{515}e^{4} - \frac{8542}{1545}e^{3} + \frac{150959}{1545}e^{2} + \frac{15989}{515}e - \frac{12391}{515}$
73 $[73, 73, -w^{3} + 5w - 1]$ $-\frac{1012}{1545}e^{8} + \frac{88}{103}e^{7} + \frac{9158}{515}e^{6} - \frac{1163}{103}e^{5} - \frac{71778}{515}e^{4} + \frac{806}{1545}e^{3} + \frac{418913}{1545}e^{2} + \frac{41668}{515}e - \frac{31762}{515}$
79 $[79, 79, 2w^{2} + w - 6]$ $-\frac{1036}{1545}e^{8} + \frac{437}{515}e^{7} + \frac{28231}{1545}e^{6} - \frac{17051}{1545}e^{5} - \frac{74027}{515}e^{4} - \frac{822}{515}e^{3} + \frac{86890}{309}e^{2} + \frac{40529}{515}e - \frac{7077}{103}$
79 $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ $\phantom{-}\frac{251}{1545}e^{8} - \frac{202}{1545}e^{7} - \frac{468}{103}e^{6} + \frac{449}{515}e^{5} + \frac{11195}{309}e^{4} + \frac{1233}{103}e^{3} - \frac{103691}{1545}e^{2} - \frac{17164}{515}e + \frac{3304}{515}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{2} + w + 2]$ $1$