↑

Properties

Label 31734.2.a.m
Level $31734$
Weight $2$
Character orbit 31734.a
Self dual yes
Analytic conductor $253.397$
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] = [31734,2,Mod(1,31734)] 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("31734.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31734, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 31734 = 2 \cdot 3^{2} \cdot 41 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 31734.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,0,1,1,0,-3,1,0,1,3,0,-5,-3,0,1,2,0,-5,1,0,3,8,0,-4,-5,0, -3,7,0,-4,1,0,2,-3,0,8,-5,0,1,1,0,-1,3,0,8,-3,0,2,-4,0,-5,4,0,3,-3,0,7, 8,0,-6,-4,0,1,-5,0,-4,2,0,-3,10,0,-12,8,0,-5,-9,0,16,1,0,1,-11,0,2,-1, 0,3,-18,0,15,8,0,-3,-5,0,-1,2,0,-4] 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: \(253.397265774\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{4} + q^{5} - 3 q^{7} + q^{8} + q^{10} + 3 q^{11} - 5 q^{13} - 3 q^{14} + q^{16} + 2 q^{17} - 5 q^{19} + q^{20} + 3 q^{22} + 8 q^{23} - 4 q^{25} - 5 q^{26} - 3 q^{28} + 7 q^{29} - 4 q^{31}+ \cdots + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(41\) \( -1 \)
\(43\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.