↑

Properties

Label 28830.2.a.g
Level $28830$
Weight $2$
Character orbit 28830.a
Self dual yes
Analytic conductor $230.209$
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] = [28830,2,Mod(1,28830)] 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("28830.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28830, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 28830 = 2 \cdot 3 \cdot 5 \cdot 31^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 28830.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,-1,1,-1,1,3,-1,1,1,-1,-1,0,-3,1,1,2,-1,2,-1,-3,1,-4,1,1, 0,-1,3,-7,-1,0,-1,1,-2,-3,1,4,-2,0,1,0,3,8,-1,-1,4,-6,-1,2,-1,-2,0,5,1, 1,-3,-2,7,-7,1,12,0,3,1,0,-1,-8,2,4,3,0,-1,-6,-4,-1,2,-3,0,8,-1,1,0,-9, -3,-2,-8,7,1,6,1,0,-4,0,6,-2,1,-5,-2,-1,1] 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: \(230.208709027\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 3 q^{7} - q^{8} + q^{9} + q^{10} - q^{11} - q^{12} - 3 q^{14} + q^{15} + q^{16} + 2 q^{17} - q^{18} + 2 q^{19} - q^{20} - 3 q^{21} + q^{22} - 4 q^{23}+ \cdots - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( +1 \)
\(5\) \( +1 \)
\(31\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.