↑

Properties

Label 27225.2.a.bw
Level $27225$
Weight $2$
Character orbit 27225.a
Self dual yes
Analytic conductor $217.393$
Dimension $1$

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] = [27225,2,Mod(1,27225)] 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("27225.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27225, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 27225 = 3^{2} \cdot 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 27225.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,2,0,2,0,0,-3,0,0,0,0,0,-2,-6,0,-4,6,0,5,0,0,0,-4,0,0,-4,0, -6,-6,0,-5,-8,0,12,0,0,11,10,0,0,-4,0,-4,0,0,-8,6,0,2,0,0,-4,8,0,0,0,0, -12,-2,0,-1,-10,0,-8,0,0,7,12,0,0,-10,0,-11,22,0,10,0,0,-1,0,0,-8,10,0, 0,-8,0,0,-14,0,6,-8,0,12,0,0,17,4,0,0] 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: \(217.392719503\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q + 2 q^{2} + 2 q^{4} - 3 q^{7} - 2 q^{13} - 6 q^{14} - 4 q^{16} + 6 q^{17} + 5 q^{19} - 4 q^{23} - 4 q^{26} - 6 q^{28} - 6 q^{29} - 5 q^{31} - 8 q^{32} + 12 q^{34} + 11 q^{37} + 10 q^{38} - 4 q^{41} - 4 q^{43}+ \cdots + 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(5\) \( +1 \)
\(11\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.