↑

Properties

Label 18032.2.a.ca
Level $18032$
Weight $2$
Character orbit 18032.a
Self dual yes
Analytic conductor $143.986$
Dimension $4$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [18032,2,Mod(1,18032)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("18032.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(18032, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 18032 = 2^{4} \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 18032.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,-5,0,5,0,0,0,7,0,2,0,7,0,-1,0,-3,0,-9,0,0,0,-4,0,11,0,-17, 0,-2,0,-14,0,-13,0,0,0,0,0,1,0,15,0,18,0,11,0,-21,0,0,0,-6,0,-3,0,10,0, -9,0,-16,0,1,0,0,0,2,0,17,0,5,0,1,0,4,0,-22,0,0,0,-5,0,16,0,-4,0,-54,0, 25,0,9,0,0,0,13,0,3,0,-40,0,41,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(143.986244925\)
Dimension: \(4\)
Coefficient field: 4.4.14013.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 6x^{2} + 6x + 3 \) Copy content Toggle raw display
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 4 q - 5 q^{3} + 5 q^{5} + 7 q^{9} + 2 q^{11} + 7 q^{13} - q^{15} - 3 q^{17} - 9 q^{19} - 4 q^{23} + 11 q^{25} - 17 q^{27} - 2 q^{29} - 14 q^{31} - 13 q^{33} + q^{39} + 15 q^{41} + 18 q^{43} + 11 q^{45}+ \cdots + 41 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(7\) \( -1 \)
\(23\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.