Properties

Label 20181.2.a.bz
Level $20181$
Weight $2$
Character orbit 20181.a
Self dual yes
Analytic conductor $161.146$
Dimension $9$

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] = [20181,2,Mod(1,20181)] 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("20181.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(20181, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 20181 = 3 \cdot 7 \cdot 31^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 20181.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [9,-1,9,13,-4,-1,9,-9,9,2,6,13,8,-1,-4,17,6,-1,0,-10,9,-2,4,-9, 25,14,9,13,2,2,0,-29,6,-6,-4,13,-4,0,8,-10,16,-1,18,22,-4,14,8,17,9,17, 6,2,2,-1,-20,-9,0,-12,12,-10,20,0,9,-7,-14,-2,6,-42,4,2,8,-9,32,44,25, 8,6,14,42,-26,9,26,16,13,12,-34,2,18,14,2,8,10,0,-4,-4,-29,6,-1,6,47] 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: \(161.146096319\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{9} - 15x^{7} - 2x^{6} + 62x^{5} + 14x^{4} - 82x^{3} - 14x^{2} + 24x - 4 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 9 q - q^{2} + 9 q^{3} + 13 q^{4} - 4 q^{5} - q^{6} + 9 q^{7} - 9 q^{8} + 9 q^{9} + 2 q^{10} + 6 q^{11} + 13 q^{12} + 8 q^{13} - q^{14} - 4 q^{15} + 17 q^{16} + 6 q^{17} - q^{18} - 10 q^{20} + 9 q^{21}+ \cdots + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(7\) \( -1 \)
\(31\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.