↑

Properties

Label 25806.2.a.b
Level $25806$
Weight $2$
Character orbit 25806.a
Self dual yes
Analytic conductor $206.062$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [25806,2,Mod(1,25806)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(25806, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("25806.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 25806 = 2 \cdot 3 \cdot 11 \cdot 17 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 25806.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(206.061947456\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - 2 q^{5} - q^{6} - 4 q^{7} - q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} + q^{3} + q^{4} - 2 q^{5} - q^{6} - 4 q^{7} - q^{8} + q^{9} + 2 q^{10} - q^{11} + q^{12} + 4 q^{14} - 2 q^{15} + q^{16} + q^{17} - q^{18} - 2 q^{20} - 4 q^{21} + q^{22} - q^{23} - q^{24} - q^{25} + q^{27} - 4 q^{28} - 4 q^{29} + 2 q^{30} + 2 q^{31} - q^{32} - q^{33} - q^{34} + 8 q^{35} + q^{36} + 4 q^{37} + 2 q^{40} - 2 q^{41} + 4 q^{42} - 8 q^{43} - q^{44} - 2 q^{45} + q^{46} + 2 q^{47} + q^{48} + 9 q^{49} + q^{50} + q^{51} - q^{54} + 2 q^{55} + 4 q^{56} + 4 q^{58} + 8 q^{59} - 2 q^{60} + 10 q^{61} - 2 q^{62} - 4 q^{63} + q^{64} + q^{66} + 4 q^{67} + q^{68} - q^{69} - 8 q^{70} + 4 q^{71} - q^{72} - 2 q^{73} - 4 q^{74} - q^{75} + 4 q^{77} - 4 q^{79} - 2 q^{80} + q^{81} + 2 q^{82} - 12 q^{83} - 4 q^{84} - 2 q^{85} + 8 q^{86} - 4 q^{87} + q^{88} + 6 q^{89} + 2 q^{90} - q^{92} + 2 q^{93} - 2 q^{94} - q^{96} + 2 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(11\) \( +1 \)
\(17\) \( -1 \)
\(23\) \( +1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

Twists of this newform have not been computed.