↑

Properties

Label 45738.2.a.fb
Level $45738$
Weight $2$
Character orbit 45738.a
Self dual yes
Analytic conductor $365.220$
Dimension $2$

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] = [45738,2,Mod(1,45738)] 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("45738.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45738, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 45738 = 2 \cdot 3^{3} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45738.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,2,0,2,0,0,-2,2,0,0,0,0,0,-2,0,2,1,0,10,0,0,0,8,0,0,0,0,-2, 0,0,-4,2,0,1,0,0,-7,10,0,0,-6,0,-13,0,0,8,-18,0,2,0,0,0,15,0,0,-2,0,0, -3,0,-22,-4,0,2,0,0,-13,1,0,0,11,0,-12,-7,0,10,0,0,-29,0,0,-6,-2,0,5,-13, 0,0,18,0,0,8,0,-18,10,0,10,2,0,0] 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: \(365.219768765\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{5}) \)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 2 q + 2 q^{2} + 2 q^{4} - 2 q^{7} + 2 q^{8} - 2 q^{14} + 2 q^{16} + q^{17} + 10 q^{19} + 8 q^{23} - 2 q^{28} - 4 q^{31} + 2 q^{32} + q^{34} - 7 q^{37} + 10 q^{38} - 6 q^{41} - 13 q^{43} + 8 q^{46} - 18 q^{47}+ \cdots + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(7\) \( +1 \)
\(11\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.