↑

Properties

Label 29106.2.a.b
Level $29106$
Weight $2$
Character orbit 29106.a
Self dual yes
Analytic conductor $232.413$
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] = [29106,2,Mod(1,29106)] 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("29106.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(29106, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 29106 = 2 \cdot 3^{3} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 29106.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,0,1,-3,0,0,-1,0,3,-1,0,-1,0,0,1,7,0,6,-3,0,1,5,0,4,1,0, 0,2,0,-6,-1,0,-7,0,0,-6,-6,0,3,9,0,-8,-1,0,-5,-8,0,0,-4,0,-1,-3,0,3,0, 0,-2,-4,0,9,6,0,1,3,0,-7,7,0,0,0,0,-6,6,0,6,0,0,-15,-3,0,-9,7,0,-21,8, 0,1,8,0,0,5,0,8,-18,0,5,0,0,4] 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: \(232.412580123\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{4} - 3 q^{5} - q^{8} + 3 q^{10} - q^{11} - q^{13} + q^{16} + 7 q^{17} + 6 q^{19} - 3 q^{20} + q^{22} + 5 q^{23} + 4 q^{25} + q^{26} + 2 q^{29} - 6 q^{31} - q^{32} - 7 q^{34} - 6 q^{37}+ \cdots + 5 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(7\) \( -1 \)
\(11\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.