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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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 43.d (of order \(6\), degree \(2\), minimal)

Newform invariants

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.

\(\operatorname{Tr}(f)(q) = \) \( 72q - 246q^{3} - 38122q^{4} - 3q^{5} + 8511q^{6} + 31377q^{7} + 675876q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 72q - 246q^{3} - 38122q^{4} - 3q^{5} + 8511q^{6} + 31377q^{7} + 675876q^{9} - 127061q^{10} + 521524q^{11} - 606618q^{12} + 796742q^{13} - 865794q^{14} - 433513q^{15} + 22423366q^{16} - 1768471q^{17} - 11957547q^{18} - 122844q^{19} + 419841q^{20} - 26778860q^{21} + 16414886q^{23} + 8684578q^{24} + 70516989q^{25} + 3069q^{26} - 97624092q^{28} + 118701393q^{29} - 1455921q^{30} + 10824883q^{31} + 315141798q^{33} + 47529561q^{34} - 333788722q^{35} - 597728908q^{36} - 169881246q^{37} - 88887452q^{38} + 570788831q^{40} - 543049070q^{41} + 408159179q^{43} - 754130886q^{44} + 270181896q^{46} + 348527658q^{47} + 175039227q^{48} + 781091547q^{49} - 663244398q^{50} - 1853993086q^{52} + 219922736q^{53} + 3104867360q^{54} + 2154394182q^{55} + 2010912675q^{56} + 349107351q^{57} + 2023447828q^{58} + 2247595680q^{59} - 2906780465q^{60} + 508093974q^{61} - 3451752063q^{62} + 158921973q^{63} - 13473879716q^{64} + 1277847051q^{66} - 2812410281q^{67} + 13614613118q^{68} - 5113655829q^{69} + 2418191196q^{71} + 26243329290q^{72} - 6537901611q^{73} - 2632816966q^{74} - 10170994206q^{76} - 16936463889q^{77} - 24146069696q^{78} + 5397136602q^{79} + 7242149661q^{80} - 15745886176q^{81} + 4998656042q^{83} + 44726677232q^{84} - 27688564866q^{86} + 37895576172q^{87} - 12151857357q^{89} - 96024912764q^{90} + 36633770214q^{91} - 31643971023q^{92} + 59768940153q^{93} - 19802964089q^{95} - 3289705262q^{96} - 40329658574q^{97} + 19243888221q^{98} + 18506221111q^{99} + O(q^{100}) \)

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.

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 37.36
Significant digits:
Format:

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 \(S_{11}^{\mathrm{new}}(43, [\chi])\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database