↑

Properties

Label 33282.2.a.e
Level $33282$
Weight $2$
Character orbit 33282.a
Self dual yes
Analytic conductor $265.758$
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] = [33282,2,Mod(1,33282)] 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("33282.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33282, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 33282 = 2 \cdot 3^{2} \cdot 43^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 33282.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,0,1,-2,0,-2,-1,0,2,1,0,-4,2,0,1,-1,0,-1,-2,0,-1,4,0,-1, 4,0,-2,-4,0,-10,-1,0,1,4,0,-2,1,0,2,3,0,0,1,0,-4,-2,0,-3,1,0,-4,0,0,-2, 2,0,4,5,0,-8,10,0,1,8,0,-11,-1,0,-4,-12,0,-17,2,0,-1,-2,0,4,-2,0,-3,-8, 0,2,0,0,-1,-3,0,8,4,0,2,2,0,5,3,0,-1] 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: \(265.758108007\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{4} - 2 q^{5} - 2 q^{7} - q^{8} + 2 q^{10} + q^{11} - 4 q^{13} + 2 q^{14} + q^{16} - q^{17} - q^{19} - 2 q^{20} - q^{22} + 4 q^{23} - q^{25} + 4 q^{26} - 2 q^{28} - 4 q^{29} - 10 q^{31}+ \cdots + 3 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(43\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.