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Properties

Label 1881.4.a.n
Level $1881$
Weight $4$
Character orbit 1881.a
Self dual yes
Analytic conductor $110.983$
Analytic rank $1$
Dimension $23$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1881,4,Mod(1,1881)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1881, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1881.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1881 = 3^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1881.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: \(110.982592721\)
Analytic rank: \(1\)
Dimension: \(23\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 23 q - 4 q^{2} + 96 q^{4} - 14 q^{7} - 48 q^{8} - 124 q^{10} + 253 q^{11} - 150 q^{13} - 152 q^{14} + 444 q^{16} + 68 q^{17} - 437 q^{19} - 80 q^{20} - 44 q^{22} - 414 q^{23} + 383 q^{25} - 464 q^{26} - 384 q^{28}+ \cdots - 7876 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −5.51625 0 22.4290 12.5056 0 26.5097 −79.5940 0 −68.9841
1.2 −5.44577 0 21.6564 −12.7630 0 14.1692 −74.3694 0 69.5044
1.3 −4.84967 0 15.5193 5.07821 0 −27.4332 −36.4664 0 −24.6277
1.4 −4.03785 0 8.30426 18.4926 0 −30.6896 −1.22854 0 −74.6704
1.5 −3.86437 0 6.93335 −18.6357 0 18.3770 4.12194 0 72.0151
1.6 −3.55917 0 4.66767 13.9292 0 7.71246 11.8603 0 −49.5764
1.7 −2.75980 0 −0.383506 8.09155 0 12.8476 23.1368 0 −22.3311
1.8 −2.60095 0 −1.23504 −11.0151 0 −27.4794 24.0199 0 28.6498
1.9 −2.17478 0 −3.27032 −3.87793 0 −23.3092 24.5105 0 8.43364
1.10 −1.56050 0 −5.56485 −10.6391 0 30.8256 21.1679 0 16.6023
1.11 −1.38247 0 −6.08877 11.8409 0 −1.48593 19.4774 0 −16.3697
1.12 0.0446892 0 −7.99800 −0.125306 0 5.63643 −0.714939 0 −0.00559983
1.13 0.835942 0 −7.30120 5.65129 0 9.55255 −12.7909 0 4.72415
1.14 1.19481 0 −6.57244 −18.9479 0 −16.9659 −17.4112 0 −22.6391
1.15 1.41012 0 −6.01156 4.37661 0 −26.4649 −19.7580 0 6.17155
1.16 2.00341 0 −3.98634 18.6175 0 22.2095 −24.0136 0 37.2986
1.17 2.42520 0 −2.11842 −17.7335 0 22.8095 −24.5392 0 −43.0071
1.18 3.14294 0 1.87809 −1.64084 0 21.7927 −19.2408 0 −5.15705
1.19 3.80817 0 6.50217 1.32583 0 −7.58061 −5.70400 0 5.04899
1.20 3.85322 0 6.84732 11.1576 0 −16.2200 −4.44155 0 42.9927
See all 23 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.23
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(11\) \( -1 \)
\(19\) \( +1 \)

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1881.4.a.n ✓ 23
3.b odd 2 1 1881.4.a.o yes 23
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1881.4.a.n ✓ 23 1.a even 1 1 trivial
1881.4.a.o yes 23 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{23} + 4 T_{2}^{22} - 132 T_{2}^{21} - 512 T_{2}^{20} + 7417 T_{2}^{19} + 27748 T_{2}^{18} + \cdots + 479213568 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1881))\). Copy content Toggle raw display