Properties

Label 4.4.9225.1-25.1-g
Base field 4.4.9225.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, \frac{1}{2}w^{3} - 3w - \frac{1}{2}]$
Dimension $14$
CM no
Base change yes

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Base field 4.4.9225.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 10x^{2} + 7x + 19\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[25, 5, \frac{1}{2}w^{3} - 3w - \frac{1}{2}]$
Dimension: $14$
CM: no
Base change: yes
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

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

\(x^{14} - 128x^{12} + 6276x^{10} - 145200x^{8} + 1553088x^{6} - 6142208x^{4} + 4468736x^{2} - 589824\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{3}{4}]$ $\phantom{-}\frac{359}{31522816}e^{12} - \frac{9013}{7880704}e^{10} + \frac{325699}{7880704}e^{8} - \frac{635735}{985088}e^{6} + \frac{2047863}{492544}e^{4} - \frac{284381}{30784}e^{2} + \frac{7507}{1924}$
4 $[4, 2, \frac{1}{2}w^{3} - 4w - \frac{1}{2}]$ $\phantom{-}\frac{359}{31522816}e^{12} - \frac{9013}{7880704}e^{10} + \frac{325699}{7880704}e^{8} - \frac{635735}{985088}e^{6} + \frac{2047863}{492544}e^{4} - \frac{284381}{30784}e^{2} + \frac{7507}{1924}$
9 $[9, 3, \frac{1}{2}w^{3} + w^{2} - 3w - \frac{7}{2}]$ $\phantom{-}e$
11 $[11, 11, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{7}{4}]$ $\phantom{-}\frac{349}{189136896}e^{13} - \frac{13103}{47284224}e^{11} + \frac{243227}{15761408}e^{9} - \frac{775043}{1970176}e^{7} + \frac{4406167}{985088}e^{5} - \frac{3238487}{184704}e^{3} + \frac{77615}{11544}e$
11 $[11, 11, \frac{1}{2}w^{3} - 4w - \frac{3}{2}]$ $\phantom{-}\frac{349}{189136896}e^{13} - \frac{13103}{47284224}e^{11} + \frac{243227}{15761408}e^{9} - \frac{775043}{1970176}e^{7} + \frac{4406167}{985088}e^{5} - \frac{3238487}{184704}e^{3} + \frac{77615}{11544}e$
19 $[19, 19, w]$ $-\frac{61}{31522816}e^{12} + \frac{63}{7880704}e^{10} + \frac{84687}{7880704}e^{8} - \frac{473471}{985088}e^{6} + \frac{3501803}{492544}e^{4} - \frac{966865}{30784}e^{2} + \frac{21791}{1924}$
19 $[19, 19, \frac{1}{4}w^{3} - \frac{5}{2}w + \frac{1}{4}]$ $-\frac{61}{31522816}e^{12} + \frac{63}{7880704}e^{10} + \frac{84687}{7880704}e^{8} - \frac{473471}{985088}e^{6} + \frac{3501803}{492544}e^{4} - \frac{966865}{30784}e^{2} + \frac{21791}{1924}$
25 $[25, 5, \frac{1}{2}w^{3} - 3w - \frac{1}{2}]$ $-1$
29 $[29, 29, \frac{3}{4}w^{3} + w^{2} - \frac{9}{2}w - \frac{25}{4}]$ $-\frac{3649}{189136896}e^{13} + \frac{94859}{47284224}e^{11} - \frac{1211607}{15761408}e^{9} + \frac{2624055}{1970176}e^{7} - \frac{10205219}{985088}e^{5} + \frac{5588879}{184704}e^{3} - \frac{79037}{11544}e$
29 $[29, 29, \frac{1}{2}w^{3} - w^{2} - 3w + \frac{9}{2}]$ $-\frac{3649}{189136896}e^{13} + \frac{94859}{47284224}e^{11} - \frac{1211607}{15761408}e^{9} + \frac{2624055}{1970176}e^{7} - \frac{10205219}{985088}e^{5} + \frac{5588879}{184704}e^{3} - \frac{79037}{11544}e$
41 $[41, 41, -w^{3} + 7w + 3]$ $-\frac{1307}{47284224}e^{13} + \frac{36865}{11821056}e^{11} - \frac{524957}{3940352}e^{9} + \frac{1312689}{492544}e^{7} - \frac{6082021}{246272}e^{5} + \frac{1966823}{23088}e^{3} - \frac{124321}{2886}e$
41 $[41, 41, -\frac{3}{4}w^{3} + \frac{11}{2}w - \frac{3}{4}]$ $\phantom{-}\frac{175}{63045632}e^{13} + \frac{387}{15761408}e^{11} - \frac{297205}{15761408}e^{9} + \frac{1580777}{1970176}e^{7} - \frac{11507513}{985088}e^{5} + \frac{3230333}{61568}e^{3} - \frac{119147}{3848}e$
41 $[41, 41, \frac{1}{4}w^{3} + w^{2} - \frac{5}{2}w - \frac{11}{4}]$ $\phantom{-}\frac{175}{63045632}e^{13} + \frac{387}{15761408}e^{11} - \frac{297205}{15761408}e^{9} + \frac{1580777}{1970176}e^{7} - \frac{11507513}{985088}e^{5} + \frac{3230333}{61568}e^{3} - \frac{119147}{3848}e$
71 $[71, 71, \frac{1}{2}w^{3} - 4w + \frac{5}{2}]$ $-\frac{1043}{189136896}e^{13} + \frac{6313}{47284224}e^{11} + \frac{311339}{15761408}e^{9} - \frac{1946263}{1970176}e^{7} + \frac{14470695}{985088}e^{5} - \frac{11402249}{184704}e^{3} + \frac{204335}{11544}e$
71 $[71, 71, \frac{3}{4}w^{3} + w^{2} - \frac{11}{2}w - \frac{21}{4}]$ $-\frac{1043}{189136896}e^{13} + \frac{6313}{47284224}e^{11} + \frac{311339}{15761408}e^{9} - \frac{1946263}{1970176}e^{7} + \frac{14470695}{985088}e^{5} - \frac{11402249}{184704}e^{3} + \frac{204335}{11544}e$
79 $[79, 79, \frac{1}{4}w^{3} - 2w^{2} + \frac{1}{2}w + \frac{25}{4}]$ $\phantom{-}\frac{5507}{31522816}e^{12} - \frac{131473}{7880704}e^{10} + \frac{4377487}{7880704}e^{8} - \frac{7332711}{985088}e^{6} + \frac{16784091}{492544}e^{4} - \frac{1065993}{30784}e^{2} + \frac{15151}{1924}$
79 $[79, 79, -\frac{3}{4}w^{3} + \frac{13}{2}w + \frac{9}{4}]$ $\phantom{-}\frac{5507}{31522816}e^{12} - \frac{131473}{7880704}e^{10} + \frac{4377487}{7880704}e^{8} - \frac{7332711}{985088}e^{6} + \frac{16784091}{492544}e^{4} - \frac{1065993}{30784}e^{2} + \frac{15151}{1924}$
89 $[89, 89, -\frac{7}{4}w^{3} - w^{2} + \frac{27}{2}w + \frac{41}{4}]$ $\phantom{-}\frac{293}{94568448}e^{13} - \frac{24463}{23642112}e^{11} + \frac{629971}{7880704}e^{9} - \frac{2399255}{985088}e^{7} + \frac{15036967}{492544}e^{5} - \frac{11399767}{92352}e^{3} + \frac{309181}{5772}e$
89 $[89, 89, -\frac{7}{4}w^{3} - w^{2} + \frac{27}{2}w + \frac{33}{4}]$ $\phantom{-}\frac{293}{94568448}e^{13} - \frac{24463}{23642112}e^{11} + \frac{629971}{7880704}e^{9} - \frac{2399255}{985088}e^{7} + \frac{15036967}{492544}e^{5} - \frac{11399767}{92352}e^{3} + \frac{309181}{5772}e$
101 $[101, 101, \frac{1}{4}w^{3} + w^{2} - \frac{1}{2}w - \frac{27}{4}]$ $\phantom{-}\frac{223}{7880704}e^{13} - \frac{1609}{492544}e^{11} + \frac{282967}{1970176}e^{9} - \frac{1465553}{492544}e^{7} + \frac{3536367}{123136}e^{5} - \frac{3204493}{30784}e^{3} + \frac{110285}{1924}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$25$ $[25, 5, \frac{1}{2}w^{3} - 3w - \frac{1}{2}]$ $1$