↑

Properties

Label 36414.2.a.d
Level $36414$
Weight $2$
Character orbit 36414.a
Self dual yes
Analytic conductor $290.767$
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] = [36414,2,Mod(1,36414)] 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("36414.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(36414, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 36414 = 2 \cdot 3^{2} \cdot 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 36414.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,0,1,-3,0,-1,-1,0,3,3,0,5,1,0,1,0,0,2,-3,0,-3,6,0,4,-5,0, -1,-6,0,4,-1,0,0,3,0,-11,-2,0,3,-12,0,-1,3,0,-6,-12,0,1,-4,0,5,9,0,-9, 1,0,6,12,0,10,-4,0,1,-15,0,5,0,0,-3,0,0,7,11,0,2,-3,0,1,-3,0,12,15,0,0, 1,0,-3,-9,0,-5,6,0,12,-6,0,19,-1,0,4] 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: \(290.767253920\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{4} - 3 q^{5} - q^{7} - q^{8} + 3 q^{10} + 3 q^{11} + 5 q^{13} + q^{14} + q^{16} + 2 q^{19} - 3 q^{20} - 3 q^{22} + 6 q^{23} + 4 q^{25} - 5 q^{26} - q^{28} - 6 q^{29} + 4 q^{31} - q^{32}+ \cdots - q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(7\) \( +1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.