↑

Properties

Label 17787.2.a.l
Level $17787$
Weight $2$
Character orbit 17787.a
Self dual yes
Analytic conductor $142.030$
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] = [17787,2,Mod(1,17787)] 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("17787.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(17787, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 17787 = 3 \cdot 7^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 17787.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,1,-1,-1,-1,0,3,1,1,0,-1,-5,0,-1,-1,7,-1,6,1,0,0,-4,3,-4, 5,1,0,9,1,2,-5,0,-7,0,-1,9,-6,-5,-3,7,0,-6,0,-1,4,-2,-1,0,4,7,5,3,-1,0, 0,6,-9,-2,1,-6,-2,0,7,5,0,8,-7,-4,0,6,3,10,-9,-4,-6,0,5,-14,1,1,-7,0,0, -7,6,9,0,9,1,0,4,2,2,-6,-5,-17,0,0,4] 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: \(142.029910075\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{3} - q^{4} - q^{5} - q^{6} + 3 q^{8} + q^{9} + q^{10} - q^{12} - 5 q^{13} - q^{15} - q^{16} + 7 q^{17} - q^{18} + 6 q^{19} + q^{20} - 4 q^{23} + 3 q^{24} - 4 q^{25} + 5 q^{26}+ \cdots - 17 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

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

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.