↑

Properties

Label 27378.2.a.b
Level $27378$
Weight $2$
Character orbit 27378.a
Self dual yes
Analytic conductor $218.614$
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] = [27378,2,Mod(1,27378)] 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("27378.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27378, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 27378 = 2 \cdot 3^{4} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 27378.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,0,1,-3,0,1,-1,0,3,0,0,0,-1,0,1,-3,0,1,-3,0,0,-9,0,4,0,0, 1,-6,0,1,-1,0,3,-3,0,-5,-1,0,3,-9,0,-7,0,0,9,-3,0,-6,-4,0,0,-6,0,0,-1, 0,6,-12,0,-7,-1,0,1,0,0,1,-3,0,3,-15,0,-14,5,0,1,0,0,5,-3,0,9,3,0,9,7, 0,0,15,0,0,-9,0,3,-3,0,13,6,0,4] 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: \(218.614430654\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{4} - 3 q^{5} + q^{7} - q^{8} + 3 q^{10} - q^{14} + q^{16} - 3 q^{17} + q^{19} - 3 q^{20} - 9 q^{23} + 4 q^{25} + q^{28} - 6 q^{29} + q^{31} - q^{32} + 3 q^{34} - 3 q^{35} - 5 q^{37}+ \cdots + 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

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

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.