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Properties

Label 43.11.d.a
Level $43$
Weight $11$
Character orbit 43.d
Analytic conductor $27.320$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [43,11,Mod(7,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.7");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 43.d (of order \(6\), degree \(2\), 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: \(27.3203618650\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9} - 127061 q^{10} + 521524 q^{11} - 606618 q^{12} + 796742 q^{13} - 865794 q^{14} - 433513 q^{15} + 22423366 q^{16} - 1768471 q^{17} - 11957547 q^{18} - 122844 q^{19} + 419841 q^{20} - 26778860 q^{21} + 16414886 q^{23} + 8684578 q^{24} + 70516989 q^{25} + 3069 q^{26} - 97624092 q^{28} + 118701393 q^{29} - 1455921 q^{30} + 10824883 q^{31} + 315141798 q^{33} + 47529561 q^{34} - 333788722 q^{35} - 597728908 q^{36} - 169881246 q^{37} - 88887452 q^{38} + 570788831 q^{40} - 543049070 q^{41} + 408159179 q^{43} - 754130886 q^{44} + 270181896 q^{46} + 348527658 q^{47} + 175039227 q^{48} + 781091547 q^{49} - 663244398 q^{50} - 1853993086 q^{52} + 219922736 q^{53} + 3104867360 q^{54} + 2154394182 q^{55} + 2010912675 q^{56} + 349107351 q^{57} + 2023447828 q^{58} + 2247595680 q^{59} - 2906780465 q^{60} + 508093974 q^{61} - 3451752063 q^{62} + 158921973 q^{63} - 13473879716 q^{64} + 1277847051 q^{66} - 2812410281 q^{67} + 13614613118 q^{68} - 5113655829 q^{69} + 2418191196 q^{71} + 26243329290 q^{72} - 6537901611 q^{73} - 2632816966 q^{74} - 10170994206 q^{76} - 16936463889 q^{77} - 24146069696 q^{78} + 5397136602 q^{79} + 7242149661 q^{80} - 15745886176 q^{81} + 4998656042 q^{83} + 44726677232 q^{84} - 27688564866 q^{86} + 37895576172 q^{87} - 12151857357 q^{89} - 96024912764 q^{90} + 36633770214 q^{91} - 31643971023 q^{92} + 59768940153 q^{93} - 19802964089 q^{95} - 3289705262 q^{96} - 40329658574 q^{97} + 19243888221 q^{98} + 18506221111 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
7.1 − 61.9282i 176.385 − 101.836i −2811.11 −2896.62 + 1672.36i −6306.51 − 10923.2i 14965.1 + 8640.13i 110672.i −8783.43 + 15213.3i 103567. + 179382.i
7.2 − 60.2423i −388.590 + 224.353i −2605.13 3532.79 − 2039.66i 13515.5 + 23409.6i 1359.86 + 785.115i 95251.0i 71143.8 − 123225.i −122874. − 212823.i
7.3 − 58.5530i 358.847 − 207.180i −2404.46 4070.35 − 2350.02i −12131.0 − 21011.6i −22979.0 − 13266.9i 80829.9i 56322.9 − 97554.1i −137601. − 238331.i
7.4 − 55.4674i −88.6325 + 51.1720i −2052.63 −1275.79 + 736.579i 2838.37 + 4916.21i −14307.5 − 8260.42i 57055.3i −24287.4 + 42066.9i 40856.1 + 70764.9i
7.5 − 50.9732i 10.9453 − 6.31925i −1574.27 3081.80 − 1779.28i −322.113 − 557.915i 5344.72 + 3085.78i 28049.1i −29444.6 + 50999.6i −90695.7 − 157089.i
7.6 − 49.1410i −303.612 + 175.291i −1390.84 −4917.98 + 2839.40i 8613.96 + 14919.8i 16455.6 + 9500.64i 18027.0i 31929.0 − 55302.7i 139531. + 241675.i
7.7 − 42.2308i 235.040 − 135.700i −759.441 1173.21 − 677.354i −5730.73 − 9925.91i 26152.5 + 15099.1i − 11172.5i 7304.58 − 12651.9i −28605.2 − 49545.7i
7.8 − 41.6701i 347.294 − 200.510i −712.398 −2813.29 + 1624.26i −8355.28 − 14471.8i −3430.02 − 1980.32i − 12984.5i 50884.2 − 88134.0i 67682.9 + 117230.i
7.9 − 41.2809i −198.317 + 114.498i −680.116 422.628 − 244.004i 4726.60 + 8186.71i 5421.13 + 3129.89i − 14195.8i −3304.75 + 5723.99i −10072.7 − 17446.5i
7.10 − 35.7982i 113.973 − 65.8024i −257.513 −2374.16 + 1370.72i −2355.61 − 4080.03i −18980.1 − 10958.2i − 27438.9i −20864.6 + 36138.5i 49069.5 + 84990.8i
7.11 − 28.8579i −341.461 + 197.142i 191.221 −978.980 + 565.214i 5689.12 + 9853.84i −26555.4 − 15331.8i − 35068.7i 48205.7 − 83494.7i 16310.9 + 28251.3i
7.12 − 25.0169i 171.910 − 99.2521i 398.154 3482.07 − 2010.37i −2482.98 − 4300.65i −9759.68 − 5634.76i − 35577.9i −9822.54 + 17013.1i −50293.3 − 87110.6i
7.13 − 24.2487i −256.468 + 148.072i 436.000 1350.56 − 779.746i 3590.55 + 6219.01i 21767.9 + 12567.7i − 35403.1i 14325.9 − 24813.2i −18907.8 − 32749.3i
7.14 − 20.4162i −201.640 + 116.417i 607.178 4872.92 − 2813.38i 2376.79 + 4116.72i −6546.27 − 3779.49i − 33302.5i −2418.78 + 4189.45i −57438.7 − 99486.7i
7.15 − 19.4681i −30.6608 + 17.7020i 644.993 −4831.05 + 2789.21i 344.625 + 596.908i 9598.06 + 5541.44i − 32492.1i −28897.8 + 50052.4i 54300.5 + 94051.3i
7.16 − 13.0858i 106.382 − 61.4196i 852.763 −2217.26 + 1280.13i −803.723 − 1392.09i 8609.98 + 4970.97i − 24558.9i −21979.8 + 38070.1i 16751.5 + 29014.5i
7.17 − 6.91481i 354.999 − 204.959i 976.185 1409.18 − 813.592i −1417.25 − 2454.75i 5180.55 + 2990.99i − 13830.9i 54491.8 − 94382.6i −5625.83 − 9744.23i
7.18 − 0.266107i −177.112 + 102.255i 1023.93 −1112.32 + 642.200i 27.2109 + 47.1306i −3824.38 − 2208.01i − 544.968i −8612.15 + 14916.7i 170.894 + 295.997i
7.19 5.41302i 42.4427 − 24.5043i 994.699 1000.11 − 577.412i 132.642 + 229.743i −21227.5 − 12255.7i 10927.3i −28323.6 + 49057.9i 3125.54 + 5413.60i
7.20 7.11093i −393.634 + 227.264i 973.435 −1943.65 + 1122.17i −1616.06 − 2799.10i 8908.31 + 5143.21i 14203.6i 73773.8 − 127780.i −7979.66 − 13821.2i
See all 72 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 7.36
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
43.d odd 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 43.11.d.a ✓ 72
43.d odd 6 1 inner 43.11.d.a ✓ 72
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.11.d.a ✓ 72 1.a even 1 1 trivial
43.11.d.a ✓ 72 43.d odd 6 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{11}^{\mathrm{new}}(43, [\chi])\).