↑

Properties

Label 28050.2.a.cy
Level $28050$
Weight $2$
Character orbit 28050.a
Self dual yes
Analytic conductor $223.980$
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] = [28050,2,Mod(1,28050)] 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("28050.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28050, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 28050 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 28050.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,1,1,0,1,-4,1,1,0,1,1,-6,-4,0,1,1,1,4,0,-4,1,0,1,0,-6,1,-4, 2,0,0,1,1,1,0,1,10,4,-6,0,-10,-4,4,1,0,0,-4,1,9,0,1,-6,2,1,0,-4,4,2,0, 0,2,0,-4,1,0,1,-12,1,0,0,0,1,10,10,0,4,-4,-6,4,0,1,-10,12,-4,0,4,2,1,-14, 0,24,0,0,-4,0,1,-18,9,1,0] 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: \(223.980377670\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + q^{6} - 4 q^{7} + q^{8} + q^{9} + q^{11} + q^{12} - 6 q^{13} - 4 q^{14} + q^{16} + q^{17} + q^{18} + 4 q^{19} - 4 q^{21} + q^{22} + q^{24} - 6 q^{26} + q^{27}+ \cdots + q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(5\) \( +1 \)
\(11\) \( -1 \)
\(17\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.