↑

Properties

Label 48552.2.a.dw
Level $48552$
Weight $2$
Character orbit 48552.a
Self dual yes
Analytic conductor $387.690$
Dimension $28$

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] = [48552,2,Mod(1,48552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(48552, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("48552.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 48552 = 2^{3} \cdot 3 \cdot 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 48552.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [28,0,28,0,0,0,-28,0,28,0,8,0,8,0,0,0,0,0,12,0,-28,0,12,0,36, 0,28,0,32,0,-24,0,8,0,0,0,20,0,8,0,4,0,0,0,0,0,32,0,28,0,0,0,20,0,56,0, 12,0,8,0,-8,0,-28,0,16,0,12,0,12,0,32,0,-44,0,36,0,-8,0,-4,0,28,0,20,0, 0,0,32,0,-28,0,-8,0,-24,0,20,0,-12,0,8,0] 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: \(387.689671894\)
Dimension: \(28\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 28 q^{3} - 28 q^{7} + 28 q^{9} + 8 q^{11} + 8 q^{13} + 12 q^{19} - 28 q^{21} + 12 q^{23} + 36 q^{25} + 28 q^{27} + 32 q^{29} - 24 q^{31} + 8 q^{33} + 20 q^{37} + 8 q^{39} + 4 q^{41} + 32 q^{47} + 28 q^{49}+ \cdots + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(7\) \( +1 \)
\(17\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.