↑

Properties

Label 37030.2.a.q
Level $37030$
Weight $2$
Character orbit 37030.a
Self dual yes
Analytic conductor $295.686$
Dimension $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [37030,2,Mod(1,37030)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(37030, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("37030.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 37030 = 2 \cdot 5 \cdot 7 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 37030.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: \(295.686038685\)
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

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{4} - q^{5} + q^{7} + q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + q^{4} - q^{5} + q^{7} + q^{8} - 3 q^{9} - q^{10} + 4 q^{11} - 2 q^{13} + q^{14} + q^{16} + 6 q^{17} - 3 q^{18} + 4 q^{19} - q^{20} + 4 q^{22} + q^{25} - 2 q^{26} + q^{28} - 2 q^{29} + 4 q^{31} + q^{32} + 6 q^{34} - q^{35} - 3 q^{36} + 2 q^{37} + 4 q^{38} - q^{40} - 6 q^{41} + 8 q^{43} + 4 q^{44} + 3 q^{45} + 8 q^{47} + q^{49} + q^{50} - 2 q^{52} - 14 q^{53} - 4 q^{55} + q^{56} - 2 q^{58} + 12 q^{59} - 6 q^{61} + 4 q^{62} - 3 q^{63} + q^{64} + 2 q^{65} + 8 q^{67} + 6 q^{68} - q^{70} - 3 q^{72} - 2 q^{73} + 2 q^{74} + 4 q^{76} + 4 q^{77} + 4 q^{79} - q^{80} + 9 q^{81} - 6 q^{82} - 4 q^{83} - 6 q^{85} + 8 q^{86} + 4 q^{88} + 6 q^{89} + 3 q^{90} - 2 q^{91} + 8 q^{94} - 4 q^{95} + 14 q^{97} + q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(5\) \( +1 \)
\(7\) \( -1 \)
\(23\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.