↑

Properties

Label 13552.2.a.dq
Level $13552$
Weight $2$
Character orbit 13552.a
Self dual yes
Analytic conductor $108.213$
Dimension $6$

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] = [13552,2,Mod(1,13552)] 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("13552.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13552, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 13552 = 2^{4} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 13552.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,0,3,0,-2,0,-6,0,-9,0,0,0,0,0,-1,0,0,0,0,0,-3,0,-4,0,22,0,-6, 0,7,0,3,0,0,0,2,0,-1,0,5,0,-5,0,21,0,3,0,-28,0,6,0,5,0,-41,0,0,0,-10,0, -2,0,19,0,9,0,0,0,-12,0,-2,0,-11,0,26,0,16,0,0,0,-12,0,-6,0,-10,0,13,0, 6,0,10,0,0,0,-1,0,-13,0,-22,0,0,0] 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: \(108.213264819\)
Dimension: \(6\)
Coefficient field: 6.6.988075625.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} - 24x^{4} + 39x^{3} + 141x^{2} - 200x - 76 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 6 q + 3 q^{3} - 2 q^{5} - 6 q^{7} - 9 q^{9} - q^{15} - 3 q^{21} - 4 q^{23} + 22 q^{25} - 6 q^{27} + 7 q^{29} + 3 q^{31} + 2 q^{35} - q^{37} + 5 q^{39} - 5 q^{41} + 21 q^{43} + 3 q^{45} - 28 q^{47} + 6 q^{49}+ \cdots - 22 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

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

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.