↑

Properties

Label 39326.2.a.bw
Level $39326$
Weight $2$
Character orbit 39326.a
Self dual yes
Analytic conductor $314.020$
Dimension $36$

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] = [39326,2,Mod(1,39326)] 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("39326.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(39326, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 39326 = 2 \cdot 7 \cdot 53^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 39326.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [36,-36,-7,36,-8,7,-36,-36,15,8,3,-7,9,36,41,36,2,-15,-30,-8, 7,-3,-3,7,18,-9,29,-36,28,-41,-21,-36,-11,-2,8,15,11,30,-7,8,-38,-7,9, 3,-34,3,44,-7,36,-18,51,9,0,-29,-31,36,-9,-28,47,41,-47,21,-15,36,-11, 11,-2,2,-11,-8,4,-15,-70,-11,-12,-30,-3,7,-49,-8,24,38,-110,7,2,-9,-30, -3,-46,34,-9,-3,-27,-44,5,7,-6,-36,26,18] 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: \(314.019690989\)
Dimension: \(36\)
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 36 q - 36 q^{2} - 7 q^{3} + 36 q^{4} - 8 q^{5} + 7 q^{6} - 36 q^{7} - 36 q^{8} + 15 q^{9} + 8 q^{10} + 3 q^{11} - 7 q^{12} + 9 q^{13} + 36 q^{14} + 41 q^{15} + 36 q^{16} + 2 q^{17} - 15 q^{18} - 30 q^{19}+ \cdots + 26 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(7\) \( +1 \)
\(53\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.