Properties

Base field 4.4.9909.1
Weight [2, 2, 2, 2]
Level norm 16
Level $[16, 2, 2]$
Label 4.4.9909.1-16.1-d
Dimension 12
CM no
Base change no

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Base field 4.4.9909.1

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

Form

Weight [2, 2, 2, 2]
Level $[16, 2, 2]$
Label 4.4.9909.1-16.1-d
Dimension 12
Is CM no
Is base change no
Parent newspace dimension 16

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{12} \) \(\mathstrut -\mathstrut 42x^{10} \) \(\mathstrut +\mathstrut 666x^{8} \) \(\mathstrut -\mathstrut 5120x^{6} \) \(\mathstrut +\mathstrut 20112x^{4} \) \(\mathstrut -\mathstrut 38240x^{2} \) \(\mathstrut +\mathstrut 27344\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-\frac{1241}{92216}e^{10} + \frac{5931}{11527}e^{8} - \frac{324291}{46108}e^{6} + \frac{983083}{23054}e^{4} - \frac{1291831}{11527}e^{2} + \frac{1153846}{11527}$
5 $[5, 5, w - 1]$ $\phantom{-}e$
7 $[7, 7, w^{3} - w^{2} - 4w + 1]$ $-\frac{73}{46108}e^{10} + \frac{2113}{46108}e^{8} - \frac{8227}{23054}e^{6} + \frac{2421}{23054}e^{4} + \frac{79916}{11527}e^{2} - \frac{170736}{11527}$
11 $[11, 11, -w^{2} + w + 2]$ $-\frac{165}{46108}e^{11} + \frac{6355}{46108}e^{9} - \frac{89141}{46108}e^{7} + \frac{144455}{11527}e^{5} - \frac{868651}{23054}e^{3} + \frac{468509}{11527}e$
13 $[13, 13, -w^{3} + w^{2} + 3w - 1]$ $-\frac{231}{46108}e^{10} + \frac{8897}{46108}e^{8} - \frac{30623}{11527}e^{6} + \frac{369893}{23054}e^{4} - \frac{457052}{11527}e^{2} + \frac{312408}{11527}$
16 $[16, 2, 2]$ $-1$
17 $[17, 17, -w^{3} + 5w + 2]$ $\phantom{-}\frac{1083}{92216}e^{11} - \frac{5083}{11527}e^{9} + \frac{67818}{11527}e^{7} - \frac{799347}{23054}e^{5} + \frac{2035167}{23054}e^{3} - \frac{854639}{11527}e$
29 $[29, 29, -w^{2} + w + 1]$ $-\frac{79}{23054}e^{11} + \frac{1696}{11527}e^{9} - \frac{53019}{23054}e^{7} + \frac{183736}{11527}e^{5} - \frac{536968}{11527}e^{3} + \frac{471617}{11527}e$
37 $[37, 37, -w^{3} + 2w^{2} + 4w - 4]$ $-\frac{73}{46108}e^{10} + \frac{2113}{46108}e^{8} - \frac{8227}{23054}e^{6} + \frac{2421}{23054}e^{4} + \frac{91443}{11527}e^{2} - \frac{239898}{11527}$
41 $[41, 41, -w^{3} + w^{2} + 5w + 1]$ $\phantom{-}\frac{423}{92216}e^{11} - \frac{3811}{23054}e^{9} + \frac{46495}{23054}e^{7} - \frac{221527}{23054}e^{5} + \frac{297865}{23054}e^{3} + \frac{82379}{11527}e$
41 $[41, 41, w^{2} - 5]$ $-\frac{79}{46108}e^{11} + \frac{848}{11527}e^{9} - \frac{53019}{46108}e^{7} + \frac{91868}{11527}e^{5} - \frac{548495}{23054}e^{3} + \frac{299207}{11527}e$
47 $[47, 47, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}\frac{197}{92216}e^{11} - \frac{4667}{46108}e^{9} + \frac{82521}{46108}e^{7} - \frac{166051}{11527}e^{5} + \frac{582367}{11527}e^{3} - \frac{670940}{11527}e$
47 $[47, 47, -w^{3} + 2w^{2} + 4w - 1]$ $\phantom{-}\frac{925}{92216}e^{11} - \frac{4235}{11527}e^{9} + \frac{218253}{46108}e^{7} - \frac{615611}{23054}e^{5} + \frac{743336}{11527}e^{3} - \frac{578486}{11527}e$
53 $[53, 53, w^{3} - 4w - 4]$ $\phantom{-}\frac{197}{92216}e^{11} - \frac{4667}{46108}e^{9} + \frac{82521}{46108}e^{7} - \frac{166051}{11527}e^{5} + \frac{582367}{11527}e^{3} - \frac{659413}{11527}e$
53 $[53, 53, 2w^{3} - 2w^{2} - 9w + 1]$ $-\frac{779}{46108}e^{11} + \frac{14827}{23054}e^{9} - \frac{201799}{23054}e^{7} + \frac{613190}{11527}e^{5} - \frac{1658031}{11527}e^{3} + \frac{1602187}{11527}e$
61 $[61, 61, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}\frac{233}{46108}e^{10} - \frac{5481}{46108}e^{8} + \frac{3892}{11527}e^{6} + \frac{149861}{23054}e^{4} - \frac{456560}{11527}e^{2} + \frac{679802}{11527}$
71 $[71, 71, w^{3} - w^{2} - 6w - 2]$ $\phantom{-}\frac{265}{92216}e^{11} - \frac{2115}{23054}e^{9} + \frac{39971}{46108}e^{7} - \frac{37791}{23054}e^{5} - \frac{125315}{11527}e^{3} + \frac{358532}{11527}e$
103 $[103, 103, 2w^{3} - 2w^{2} - 8w + 1]$ $\phantom{-}\frac{584}{11527}e^{10} - \frac{45335}{23054}e^{8} + \frac{316064}{11527}e^{6} - \frac{1963745}{11527}e^{4} + \frac{5327156}{11527}e^{2} - \frac{4933802}{11527}$
103 $[103, 103, -3w^{3} + 3w^{2} + 13w - 5]$ $\phantom{-}\frac{2119}{46108}e^{10} - \frac{80915}{46108}e^{8} + \frac{553985}{23054}e^{6} - \frac{3400473}{23054}e^{4} + \frac{4630238}{11527}e^{2} - \frac{4384638}{11527}$
109 $[109, 109, 2w^{3} - w^{2} - 8w - 4]$ $\phantom{-}\frac{624}{11527}e^{10} - \frac{47019}{23054}e^{8} + \frac{631685}{23054}e^{6} - \frac{1887604}{11527}e^{4} + \frac{4938985}{11527}e^{2} - \frac{4355574}{11527}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
16 $[16, 2, 2]$ $1$