↑

Properties

Label 47040.2.a.kq
Level $47040$
Weight $2$
Character orbit 47040.a
Self dual yes
Analytic conductor $375.616$
Dimension $3$

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] = [47040,2,Mod(1,47040)] 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("47040.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(47040, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 47040 = 2^{6} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 47040.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,0,-3,0,3,0,0,0,3,0,-1,0,1,0,-3,0,-8,0,1,0,0,0,-9,0,3,0,-3, 0,0,0,4,0,1,0,0,0,-15,0,-1,0,-5,0,-2,0,3,0,-11,0,0,0,8,0,1,0,-1,0,-1,0, -12,0,4,0,0,0,1,0,-10,0,9,0,2,0,0,0,-3,0,0,0,-18,0,3,0,-4,0,-8,0,0,0,-22, 0,0,0,-4,0,1,0,-8,0,-1,0] 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: \(375.616291108\)
Dimension: \(3\)
Coefficient field: 3.3.3576.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 15x + 3 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 3 q - 3 q^{3} + 3 q^{5} + 3 q^{9} - q^{11} + q^{13} - 3 q^{15} - 8 q^{17} + q^{19} - 9 q^{23} + 3 q^{25} - 3 q^{27} + 4 q^{31} + q^{33} - 15 q^{37} - q^{39} - 5 q^{41} - 2 q^{43} + 3 q^{45} - 11 q^{47}+ \cdots - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(5\) \( -1 \)
\(7\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.