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Properties

Label 1573.4.a.r
Level $1573$
Weight $4$
Character orbit 1573.a
Self dual yes
Analytic conductor $92.810$
Analytic rank $0$
Dimension $38$
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] = [1573,4,Mod(1,1573)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1573, 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("1573.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1573 = 11^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1573.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: \(92.8100044390\)
Analytic rank: \(0\)
Dimension: \(38\)
Twist minimal: no (minimal twist has level 143)
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.

\(\operatorname{Tr}(f)(q) = \) \( 38 q + 3 q^{2} + 19 q^{3} + 181 q^{4} + 52 q^{5} + 104 q^{6} + 12 q^{7} + 57 q^{8} + 477 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 38 q + 3 q^{2} + 19 q^{3} + 181 q^{4} + 52 q^{5} + 104 q^{6} + 12 q^{7} + 57 q^{8} + 477 q^{9} - 30 q^{10} + 122 q^{12} + 494 q^{13} + 181 q^{14} + 264 q^{15} + 961 q^{16} - 33 q^{17} + 28 q^{18} + 107 q^{19} + 595 q^{20} + 148 q^{21} + 840 q^{23} + 968 q^{24} + 1428 q^{25} + 39 q^{26} + 1108 q^{27} - 353 q^{28} - 162 q^{29} - 48 q^{30} + 62 q^{31} + 1204 q^{32} - 58 q^{34} - 352 q^{35} + 3357 q^{36} + 304 q^{37} + 963 q^{38} + 247 q^{39} - 571 q^{40} + 361 q^{41} + 587 q^{42} + 483 q^{43} + 1136 q^{45} - 1860 q^{46} + 2892 q^{47} + 945 q^{48} + 2270 q^{49} - 782 q^{50} - 682 q^{51} + 2353 q^{52} + 1622 q^{53} + 3273 q^{54} + 3269 q^{56} + 62 q^{57} + 1683 q^{58} + 3417 q^{59} + 4279 q^{60} - 1714 q^{61} + 508 q^{62} + 3730 q^{63} + 4823 q^{64} + 676 q^{65} + 4939 q^{67} - 3699 q^{68} + 1818 q^{69} + 592 q^{70} + 1544 q^{71} - 5570 q^{72} + 617 q^{73} - 1398 q^{74} + 5457 q^{75} + 3316 q^{76} + 1352 q^{78} - 3176 q^{79} + 5091 q^{80} + 5994 q^{81} + 1238 q^{82} + 1659 q^{83} + 5157 q^{84} + 1074 q^{85} + 1144 q^{86} - 906 q^{87} + 3727 q^{89} - 6753 q^{90} + 156 q^{91} + 11004 q^{92} + 6956 q^{93} - 9255 q^{94} + 1768 q^{95} + 4812 q^{96} + 5723 q^{97} + 2043 q^{98}+O(q^{100}) \) 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 −5.40725 −9.85335 21.2383 2.70052 53.2795 17.4417 −71.5828 70.0885 −14.6024
1.2 −5.29658 0.842159 20.0537 17.1281 −4.46056 −29.9344 −63.8434 −26.2908 −90.7205
1.3 −5.00760 9.86483 17.0761 7.04367 −49.3991 10.9844 −45.4495 70.3148 −35.2719
1.4 −4.91880 6.32558 16.1946 14.5424 −31.1143 −10.8097 −40.3078 13.0129 −71.5310
1.5 −4.77612 −6.98510 14.8113 −18.7824 33.3617 −19.3562 −32.5316 21.7917 89.7068
1.6 −4.36004 −7.06545 11.0100 13.4149 30.8057 −26.3473 −13.1237 22.9207 −58.4897
1.7 −4.27964 5.37197 10.3154 −15.4176 −22.9901 −2.12499 −9.90888 1.85803 65.9820
1.8 −3.73641 −4.86311 5.96075 −13.0752 18.1706 −14.7601 7.61947 −3.35018 48.8542
1.9 −3.59807 −0.839024 4.94611 −13.6879 3.01887 14.6778 10.9881 −26.2960 49.2501
1.10 −3.40898 −4.61605 3.62112 16.4576 15.7360 17.8059 14.9275 −5.69212 −56.1036
1.11 −3.37023 0.655105 3.35847 7.15285 −2.20786 33.9288 15.6430 −26.5708 −24.1068
1.12 −2.30795 2.85919 −2.67337 −13.3592 −6.59888 24.3416 24.6336 −18.8250 30.8324
1.13 −2.27170 9.74279 −2.83939 7.38773 −22.1327 −14.7359 24.6238 67.9220 −16.7827
1.14 −1.44591 0.469802 −5.90935 0.718882 −0.679291 −29.1536 20.1116 −26.7793 −1.03944
1.15 −1.24551 −7.41151 −6.44870 21.2802 9.23113 11.3706 17.9960 27.9304 −26.5048
1.16 −1.11203 0.728807 −6.76339 6.16953 −0.810455 4.11690 16.4173 −26.4688 −6.86070
1.17 −0.778763 8.75573 −7.39353 18.5519 −6.81864 1.58865 11.9879 49.6628 −14.4475
1.18 −0.582982 −4.74799 −7.66013 −1.95618 2.76800 0.377004 9.12958 −4.45657 1.14042
1.19 −0.453664 6.65479 −7.79419 −5.35620 −3.01904 27.7636 7.16526 17.2862 2.42992
1.20 −0.336372 −8.24445 −7.88685 −6.61521 2.77321 −10.8382 5.34390 40.9710 2.22517
See all 38 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.38
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 1573.4.a.r 38
11.b odd 2 1 1573.4.a.q 38
11.d odd 10 2 143.4.h.b ✓ 76
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
143.4.h.b ✓ 76 11.d odd 10 2
1573.4.a.q 38 11.b odd 2 1
1573.4.a.r 38 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{38} - 3 T_{2}^{37} - 238 T_{2}^{36} + 688 T_{2}^{35} + 25878 T_{2}^{34} - 71961 T_{2}^{33} + \cdots + 34\!\cdots\!64 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1573))\). Copy content Toggle raw display