↑

Properties

Label 1587.4.a.v
Level $1587$
Weight $4$
Character orbit 1587.a
Self dual yes
Analytic conductor $93.636$
Analytic rank $1$
Dimension $30$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1587,4,Mod(1,1587)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1587, 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("1587.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1587 = 3 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1587.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: \(93.6360311791\)
Analytic rank: \(1\)
Dimension: \(30\)
Twist minimal: no (minimal twist has level 69)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 30 q + 2 q^{2} - 90 q^{3} + 118 q^{4} - 52 q^{5} - 6 q^{6} + 2 q^{7} + 18 q^{8} + 270 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 30 q + 2 q^{2} - 90 q^{3} + 118 q^{4} - 52 q^{5} - 6 q^{6} + 2 q^{7} + 18 q^{8} + 270 q^{9} + 39 q^{10} - 126 q^{11} - 354 q^{12} + 14 q^{13} - 42 q^{14} + 156 q^{15} + 438 q^{16} - 340 q^{17} + 18 q^{18} + 156 q^{19} - 617 q^{20} - 6 q^{21} - 311 q^{22} - 54 q^{24} + 624 q^{25} + 398 q^{26} - 810 q^{27} - 468 q^{28} - 196 q^{29} - 117 q^{30} - 380 q^{31} + 46 q^{32} + 378 q^{33} - 64 q^{34} - 636 q^{35} + 1062 q^{36} - 1082 q^{37} - 747 q^{38} - 42 q^{39} + 623 q^{40} + 768 q^{41} + 126 q^{42} - 68 q^{43} - 1657 q^{44} - 468 q^{45} - 720 q^{47} - 1314 q^{48} + 2926 q^{49} - 1008 q^{50} + 1020 q^{51} + 482 q^{52} - 2720 q^{53} - 54 q^{54} - 336 q^{55} - 576 q^{56} - 468 q^{57} - 690 q^{58} + 80 q^{59} + 1851 q^{60} - 906 q^{61} - 110 q^{62} + 18 q^{63} + 5740 q^{64} - 3490 q^{65} + 933 q^{66} - 1294 q^{67} - 2802 q^{68} + 1492 q^{70} - 1350 q^{71} + 162 q^{72} - 1824 q^{73} - 2629 q^{74} - 1872 q^{75} + 585 q^{76} - 864 q^{77} - 1194 q^{78} + 3540 q^{79} - 5233 q^{80} + 2430 q^{81} + 2166 q^{82} - 1410 q^{83} + 1404 q^{84} + 2468 q^{85} - 1597 q^{86} + 588 q^{87} - 5645 q^{88} - 2022 q^{89} + 351 q^{90} + 2718 q^{91} + 1140 q^{93} - 1548 q^{94} + 9230 q^{95} - 138 q^{96} - 2926 q^{97} - 11775 q^{98} - 1134 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −5.58501 −3.00000 23.1923 −6.30398 16.7550 15.3707 −84.8493 9.00000 35.2078
1.2 −5.10292 −3.00000 18.0398 −10.4125 15.3088 −33.1151 −51.2323 9.00000 53.1343
1.3 −4.82763 −3.00000 15.3060 −18.5088 14.4829 29.6112 −35.2709 9.00000 89.3539
1.4 −4.51388 −3.00000 12.3751 16.0244 13.5416 1.96414 −19.7486 9.00000 −72.3321
1.5 −4.20880 −3.00000 9.71398 9.07869 12.6264 −20.8523 −7.21382 9.00000 −38.2104
1.6 −3.90585 −3.00000 7.25568 −2.82752 11.7176 −35.5408 2.90722 9.00000 11.0439
1.7 −3.27212 −3.00000 2.70675 −4.73753 9.81635 21.7727 17.3201 9.00000 15.5017
1.8 −2.84814 −3.00000 0.111892 −1.27489 8.54442 −2.82144 22.4664 9.00000 3.63106
1.9 −2.39239 −3.00000 −2.27649 −14.9344 7.17716 −25.5860 24.5853 9.00000 35.7289
1.10 −2.39062 −3.00000 −2.28494 −2.74217 7.17186 34.5175 24.5874 9.00000 6.55549
1.11 −2.25363 −3.00000 −2.92115 −20.4315 6.76089 22.1726 24.6122 9.00000 46.0450
1.12 −1.45801 −3.00000 −5.87421 16.2610 4.37402 −5.17485 20.2287 9.00000 −23.7086
1.13 −1.12798 −3.00000 −6.72766 19.1197 3.38394 7.08634 16.6125 9.00000 −21.5666
1.14 −0.920611 −3.00000 −7.15248 6.10935 2.76183 12.0479 13.9495 9.00000 −5.62433
1.15 −0.346571 −3.00000 −7.87989 1.16508 1.03971 30.3696 5.50351 9.00000 −0.403784
1.16 0.455677 −3.00000 −7.79236 11.5585 −1.36703 −21.1208 −7.19622 9.00000 5.26695
1.17 0.537975 −3.00000 −7.71058 −15.9326 −1.61392 −30.2095 −8.45189 9.00000 −8.57134
1.18 1.62611 −3.00000 −5.35578 −3.75631 −4.87832 −14.9867 −21.7179 9.00000 −6.10816
1.19 1.76617 −3.00000 −4.88065 −18.6788 −5.29850 −8.71734 −22.7494 9.00000 −32.9898
1.20 2.29359 −3.00000 −2.73946 −17.3458 −6.88076 26.1011 −24.6319 9.00000 −39.7841
See all 30 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.30
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(23\) \(-1\)

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 1587.4.a.v 30
23.b odd 2 1 1587.4.a.w 30
23.d odd 22 2 69.4.e.b ✓ 60
69.g even 22 2 207.4.i.b 60
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
69.4.e.b ✓ 60 23.d odd 22 2
207.4.i.b 60 69.g even 22 2
1587.4.a.v 30 1.a even 1 1 trivial
1587.4.a.w 30 23.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1587))\):

\( T_{2}^{30} - 2 T_{2}^{29} - 177 T_{2}^{28} + 340 T_{2}^{27} + 13919 T_{2}^{26} - 25550 T_{2}^{25} + \cdots - 931503625216 \) Copy content Toggle raw display
\( T_{5}^{30} + 52 T_{5}^{29} - 835 T_{5}^{28} - 83724 T_{5}^{27} - 234317 T_{5}^{26} + \cdots - 71\!\cdots\!39 \) Copy content Toggle raw display