Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [21294,2,Mod(1,21294)] 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("21294.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(21294, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 21294 = 2 \cdot 3^{2} \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 21294.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,0,1,0,0,-1,1,0,0,-6,0,0,-1,0,1,3,0,-8,0,0,-6,-3,0,-5,0,0, -1,6,0,7,1,0,3,0,0,-8,-8,0,0,-6,0,5,-6,0,-3,0,0,1,-5,0,0,-9,0,0,-1,0,6, 15,0,5,7,0,1,0,0,7,3,0,0,-3,0,-8,-8,0,-8,6,0,14,0,0,-6,-9,0,0,5,0,-6,-15, 0,0,-3,0,0,0,0,4,1,0,-5] 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: \(170.033446064\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{4} - q^{7} + q^{8} - 6 q^{11} - q^{14} + q^{16} + 3 q^{17} - 8 q^{19} - 6 q^{22} - 3 q^{23} - 5 q^{25} - q^{28} + 6 q^{29} + 7 q^{31} + q^{32} + 3 q^{34} - 8 q^{37} - 8 q^{38} - 6 q^{41}+ \cdots + q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(7\) \( +1 \)
\(13\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.