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Properties

Label 1859.4.a.l
Level $1859$
Weight $4$
Character orbit 1859.a
Self dual yes
Analytic conductor $109.685$
Analytic rank $1$
Dimension $36$
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] = [1859,4,Mod(1,1859)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1859.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1859.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: \(109.684550701\)
Analytic rank: \(1\)
Dimension: \(36\)
Twist minimal: no (minimal twist has level 143)
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.

\(\operatorname{Tr}(f)(q) = \) \( 36 q - 4 q^{2} + 12 q^{3} + 152 q^{4} - 40 q^{5} - 98 q^{6} - 56 q^{7} - 84 q^{8} + 360 q^{9} - 56 q^{10} - 396 q^{11} + 66 q^{12} + 164 q^{14} - 120 q^{15} + 644 q^{16} + 138 q^{17} + 28 q^{18} - 498 q^{19}+ \cdots - 3960 q^{99}+O(q^{100}) \) 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 −5.40970 9.04984 21.2648 14.9789 −48.9569 −21.1440 −71.7586 54.8996 −81.0315
1.2 −5.37051 6.42352 20.8423 −1.04643 −34.4976 −14.1100 −68.9699 14.2616 5.61984
1.3 −5.31556 −6.97612 20.2552 −11.0780 37.0820 −15.5383 −65.1431 21.6662 58.8858
1.4 −4.91072 4.96902 16.1152 −14.5097 −24.4015 24.8330 −39.8514 −2.30886 71.2531
1.5 −4.68862 −2.64231 13.9831 −16.8988 12.3888 −13.2904 −28.0526 −20.0182 79.2322
1.6 −4.48294 −3.05507 12.0967 15.8460 13.6957 14.1972 −18.3654 −17.6666 −71.0368
1.7 −3.97184 1.90642 7.77550 18.9601 −7.57198 23.8934 0.891668 −23.3656 −75.3066
1.8 −3.52500 6.60993 4.42564 −15.7848 −23.3000 −35.5340 12.5996 16.6911 55.6415
1.9 −3.45591 −5.41746 3.94332 9.57590 18.7223 −27.8655 14.0195 2.34888 −33.0934
1.10 −3.25823 −8.58536 2.61606 2.74949 27.9731 −10.9805 17.5421 46.7084 −8.95848
1.11 −3.04437 6.04232 1.26822 6.26745 −18.3951 22.1223 20.4941 9.50964 −19.0805
1.12 −2.93776 9.49640 0.630432 −20.5709 −27.8981 −4.19587 21.6500 63.1815 60.4323
1.13 −2.56135 −1.18355 −1.43947 −4.85042 3.03148 6.35045 24.1778 −25.5992 12.4237
1.14 −1.74560 −4.37143 −4.95287 −9.81487 7.63078 18.0536 22.6106 −7.89058 17.1329
1.15 −1.63327 3.36108 −5.33243 4.44226 −5.48955 −30.4921 21.7754 −15.7031 −7.25541
1.16 −0.851378 5.53627 −7.27515 7.50257 −4.71346 8.31728 13.0049 3.65026 −6.38753
1.17 −0.236535 −7.74253 −7.94405 11.7890 1.83138 5.71517 3.77132 32.9468 −2.78850
1.18 0.231915 8.68804 −7.94622 −0.297636 2.01489 −7.88297 −3.69817 48.4820 −0.0690264
1.19 0.665052 −3.21477 −7.55771 −10.5229 −2.13799 −28.9946 −10.3467 −16.6653 −6.99830
1.20 0.677132 5.62189 −7.54149 21.4343 3.80677 −10.4645 −10.5236 4.60569 14.5139
See all 36 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.36
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(11\) \( +1 \)
\(13\) \( -1 \)

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 1859.4.a.l 36
13.b even 2 1 1859.4.a.m 36
13.f odd 12 2 143.4.j.a ✓ 72
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
143.4.j.a ✓ 72 13.f odd 12 2
1859.4.a.l 36 1.a even 1 1 trivial
1859.4.a.m 36 13.b even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{36} + 4 T_{2}^{35} - 212 T_{2}^{34} - 820 T_{2}^{33} + 20423 T_{2}^{32} + 75918 T_{2}^{31} + \cdots - 43206514311168 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1859))\). Copy content Toggle raw display