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Properties

Label 1890.2.bq.a
Level $1890$
Weight $2$
Character orbit 1890.bq
Analytic conductor $15.092$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1890,2,Mod(289,1890)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1890, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1890.289");
 
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.bq (of order \(6\), degree \(2\), not 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: \(96\)
Relative dimension: \(48\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q + 48 q^{4}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 96 q + 48 q^{4} + 8 q^{11} + 2 q^{14} - 48 q^{16} - 24 q^{26} - 10 q^{29} + 34 q^{35} - 30 q^{41} + 4 q^{44} - 6 q^{46} + 12 q^{49} + 12 q^{50} + 12 q^{55} + 4 q^{56} + 24 q^{59} - 6 q^{61} - 96 q^{64} - 18 q^{65} + 6 q^{70} + 32 q^{71} + 8 q^{86} + 66 q^{89} - 12 q^{94} - 30 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
289.1 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 1.49821 − 1.65993i 0 −0.276001 − 2.63132i 1.00000i 0 −0.467519 + 2.18665i
289.2 −0.866025 + 0.500000i 0 0.500000 − 0.866025i −1.35071 + 1.78202i 0 2.26891 − 1.36089i 1.00000i 0 0.278738 − 2.21863i
289.3 −0.866025 + 0.500000i 0 0.500000 − 0.866025i −1.89610 + 1.18525i 0 −0.873692 + 2.49733i 1.00000i 0 1.04945 − 1.97450i
289.4 −0.866025 + 0.500000i 0 0.500000 − 0.866025i −1.55413 − 1.60770i 0 2.57509 + 0.607380i 1.00000i 0 2.14976 + 0.615245i
289.5 −0.866025 + 0.500000i 0 0.500000 − 0.866025i −1.41556 + 1.73095i 0 −1.74017 − 1.99294i 1.00000i 0 0.360436 − 2.20683i
289.6 −0.866025 + 0.500000i 0 0.500000 − 0.866025i −2.17928 − 0.500735i 0 1.03354 − 2.43553i 1.00000i 0 2.13768 − 0.655991i
289.7 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 0.409739 + 2.19821i 0 1.55043 + 2.14387i 1.00000i 0 −1.45395 − 1.69883i
289.8 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 0.750434 − 2.10638i 0 −2.48341 + 0.912521i 1.00000i 0 0.403297 + 2.19940i
289.9 −0.866025 + 0.500000i 0 0.500000 − 0.866025i −0.730833 + 2.11326i 0 0.600499 − 2.57670i 1.00000i 0 −0.423712 − 2.19556i
289.10 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 0.557856 − 2.16536i 0 −0.346870 + 2.62291i 1.00000i 0 0.599564 + 2.15419i
289.11 −0.866025 + 0.500000i 0 0.500000 − 0.866025i −0.354381 − 2.20781i 0 −1.56393 + 2.13404i 1.00000i 0 1.41081 + 1.73483i
289.12 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 1.78400 + 1.34809i 0 2.32863 − 1.25598i 1.00000i 0 −2.21903 − 0.275481i
289.13 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 0.688958 − 2.12728i 0 2.47408 + 0.937525i 1.00000i 0 0.466987 + 2.18676i
289.14 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 2.20249 + 0.386083i 0 1.03562 + 2.43465i 1.00000i 0 −2.10045 + 0.766885i
289.15 −0.866025 + 0.500000i 0 0.500000 − 0.866025i −1.70959 + 1.44129i 0 2.11221 + 1.59329i 1.00000i 0 0.759902 − 2.10299i
289.16 −0.866025 + 0.500000i 0 0.500000 − 0.866025i −1.82669 − 1.28965i 0 −2.61855 + 0.378415i 1.00000i 0 2.22679 + 0.203520i
289.17 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 2.23165 − 0.140481i 0 −0.387288 + 2.61725i 1.00000i 0 −1.86243 + 1.23749i
289.18 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 2.15250 − 0.605607i 0 1.94150 − 1.79738i 1.00000i 0 −1.56131 + 1.60072i
289.19 −0.866025 + 0.500000i 0 0.500000 − 0.866025i −0.412019 + 2.19778i 0 −2.44216 + 1.01778i 1.00000i 0 −0.742071 − 2.10934i
289.20 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 0.928700 + 2.03409i 0 −2.46103 − 0.971242i 1.00000i 0 −1.82132 − 1.29722i
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 289.48
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
63.g even 3 1 inner
315.bo even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1890.2.bq.a 96
3.b odd 2 1 630.2.bq.a yes 96
5.b even 2 1 inner 1890.2.bq.a 96
7.c even 3 1 1890.2.ba.a 96
9.c even 3 1 1890.2.ba.a 96
9.d odd 6 1 630.2.ba.a ✓ 96
15.d odd 2 1 630.2.bq.a yes 96
21.h odd 6 1 630.2.ba.a ✓ 96
35.j even 6 1 1890.2.ba.a 96
45.h odd 6 1 630.2.ba.a ✓ 96
45.j even 6 1 1890.2.ba.a 96
63.g even 3 1 inner 1890.2.bq.a 96
63.n odd 6 1 630.2.bq.a yes 96
105.o odd 6 1 630.2.ba.a ✓ 96
315.v odd 6 1 630.2.bq.a yes 96
315.bo even 6 1 inner 1890.2.bq.a 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
630.2.ba.a ✓ 96 9.d odd 6 1
630.2.ba.a ✓ 96 21.h odd 6 1
630.2.ba.a ✓ 96 45.h odd 6 1
630.2.ba.a ✓ 96 105.o odd 6 1
630.2.bq.a yes 96 3.b odd 2 1
630.2.bq.a yes 96 15.d odd 2 1
630.2.bq.a yes 96 63.n odd 6 1
630.2.bq.a yes 96 315.v odd 6 1
1890.2.ba.a 96 7.c even 3 1
1890.2.ba.a 96 9.c even 3 1
1890.2.ba.a 96 35.j even 6 1
1890.2.ba.a 96 45.j even 6 1
1890.2.bq.a 96 1.a even 1 1 trivial
1890.2.bq.a 96 5.b even 2 1 inner
1890.2.bq.a 96 63.g even 3 1 inner
1890.2.bq.a 96 315.bo even 6 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1890, [\chi])\).