↑

Properties

Label 1890.2.m.b
Level $1890$
Weight $2$
Character orbit 1890.m
Analytic conductor $15.092$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1890,2,Mod(323,1890)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1890, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1890.323");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1890.m (of order \(4\), degree \(2\), minimal)

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: no
Analytic conductor: \(15.0917259820\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{5} - 24 q^{13} + 24 q^{14} - 24 q^{16} + 16 q^{17} - 4 q^{22} + 4 q^{25} + 8 q^{29} + 8 q^{31} - 8 q^{35} - 4 q^{37} - 4 q^{38} + 8 q^{40} + 16 q^{43} - 16 q^{44} - 8 q^{46} - 32 q^{47} - 16 q^{50} + 24 q^{52} + 48 q^{53} - 32 q^{55} + 8 q^{58} + 32 q^{59} + 28 q^{62} + 48 q^{65} - 16 q^{68} - 4 q^{70} + 24 q^{73} + 8 q^{74} + 4 q^{77} + 4 q^{80} - 8 q^{82} - 24 q^{83} + 12 q^{85} - 4 q^{88} - 96 q^{89} - 72 q^{95} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
323.1 −0.707107 − 0.707107i 0 1.00000i 0.419422 + 2.19638i 0 −0.707107 + 0.707107i 0.707107 − 0.707107i 0 1.25650 − 1.84965i
323.2 −0.707107 − 0.707107i 0 1.00000i 1.94482 + 1.10348i 0 −0.707107 + 0.707107i 0.707107 − 0.707107i 0 −0.594917 − 2.15548i
323.3 −0.707107 − 0.707107i 0 1.00000i 0.283889 − 2.21797i 0 −0.707107 + 0.707107i 0.707107 − 0.707107i 0 −1.76908 + 1.36760i
323.4 −0.707107 − 0.707107i 0 1.00000i 1.98740 − 1.02482i 0 −0.707107 + 0.707107i 0.707107 − 0.707107i 0 −2.12996 − 0.680649i
323.5 −0.707107 − 0.707107i 0 1.00000i −2.02160 + 0.955573i 0 −0.707107 + 0.707107i 0.707107 − 0.707107i 0 2.10518 + 0.753797i
323.6 −0.707107 − 0.707107i 0 1.00000i −2.19971 + 0.401567i 0 −0.707107 + 0.707107i 0.707107 − 0.707107i 0 1.83938 + 1.27148i
323.7 0.707107 + 0.707107i 0 1.00000i −0.857378 + 2.06516i 0 0.707107 − 0.707107i −0.707107 + 0.707107i 0 −2.06655 + 0.854034i
323.8 0.707107 + 0.707107i 0 1.00000i −1.92333 + 1.14052i 0 0.707107 − 0.707107i −0.707107 + 0.707107i 0 −2.16647 − 0.553531i
323.9 0.707107 + 0.707107i 0 1.00000i −1.45741 − 1.69586i 0 0.707107 − 0.707107i −0.707107 + 0.707107i 0 0.168613 − 2.22970i
323.10 0.707107 + 0.707107i 0 1.00000i 1.10768 − 1.94243i 0 0.707107 − 0.707107i −0.707107 + 0.707107i 0 2.15676 − 0.590258i
323.11 0.707107 + 0.707107i 0 1.00000i 2.09650 + 0.777612i 0 0.707107 − 0.707107i −0.707107 + 0.707107i 0 0.932595 + 2.03231i
323.12 0.707107 + 0.707107i 0 1.00000i −1.38028 − 1.75922i 0 0.707107 − 0.707107i −0.707107 + 0.707107i 0 0.267951 − 2.21996i
1457.1 −0.707107 + 0.707107i 0 − 1.00000i 0.419422 − 2.19638i 0 −0.707107 − 0.707107i 0.707107 + 0.707107i 0 1.25650 + 1.84965i
1457.2 −0.707107 + 0.707107i 0 − 1.00000i 1.94482 − 1.10348i 0 −0.707107 − 0.707107i 0.707107 + 0.707107i 0 −0.594917 + 2.15548i
1457.3 −0.707107 + 0.707107i 0 − 1.00000i 0.283889 + 2.21797i 0 −0.707107 − 0.707107i 0.707107 + 0.707107i 0 −1.76908 − 1.36760i
1457.4 −0.707107 + 0.707107i 0 − 1.00000i 1.98740 + 1.02482i 0 −0.707107 − 0.707107i 0.707107 + 0.707107i 0 −2.12996 + 0.680649i
1457.5 −0.707107 + 0.707107i 0 − 1.00000i −2.02160 − 0.955573i 0 −0.707107 − 0.707107i 0.707107 + 0.707107i 0 2.10518 − 0.753797i
1457.6 −0.707107 + 0.707107i 0 − 1.00000i −2.19971 − 0.401567i 0 −0.707107 − 0.707107i 0.707107 + 0.707107i 0 1.83938 − 1.27148i
1457.7 0.707107 − 0.707107i 0 − 1.00000i −0.857378 − 2.06516i 0 0.707107 + 0.707107i −0.707107 − 0.707107i 0 −2.06655 − 0.854034i
1457.8 0.707107 − 0.707107i 0 − 1.00000i −1.92333 − 1.14052i 0 0.707107 + 0.707107i −0.707107 − 0.707107i 0 −2.16647 + 0.553531i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 323.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
15.e even 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1890.2.m.b ✓ 24
3.b odd 2 1 1890.2.m.c yes 24
5.c odd 4 1 1890.2.m.c yes 24
15.e even 4 1 inner 1890.2.m.b ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1890.2.m.b ✓ 24 1.a even 1 1 trivial
1890.2.m.b ✓ 24 15.e even 4 1 inner
1890.2.m.c yes 24 3.b odd 2 1
1890.2.m.c yes 24 5.c odd 4 1