Properties

Label 43.9.b.b
Level 43
Weight 9
Character orbit 43.b
Analytic conductor 17.517
Analytic rank 0
Dimension 28
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.5172802326\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + 24982q^{10} + 4538q^{11} + 22086q^{13} + 24732q^{14} + 15388q^{15} + 525812q^{16} - 135136q^{17} - 261352q^{21} - 184432q^{23} + 1770326q^{24} - 2640434q^{25} - 110272q^{31} + 10947816q^{35} + 11602066q^{36} - 7189158q^{38} - 21389338q^{40} + 1301336q^{41} + 2473420q^{43} - 8818480q^{44} + 1983566q^{47} - 15560936q^{49} + 12927876q^{52} + 23942594q^{53} - 13757972q^{54} + 34967256q^{56} + 35225148q^{57} + 22565734q^{58} - 5554336q^{59} - 44902072q^{60} - 170444572q^{64} - 48457584q^{66} - 130953802q^{67} + 150021122q^{68} + 205870278q^{74} + 267860612q^{78} + 7380250q^{79} - 57601004q^{81} - 42603970q^{83} + 251931292q^{84} - 45482652q^{86} - 106687410q^{87} - 255044692q^{90} - 409532014q^{92} + 123322986q^{95} - 692987086q^{96} - 318744840q^{97} - 609707206q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
42.1 31.2764i 113.679i −722.216 959.913i −3555.47 3354.89i 14581.6i −6361.87 30022.7
42.2 31.0929i 76.9602i −710.770 309.101i 2392.92 1604.82i 14140.1i 638.125 −9610.84
42.3 25.4156i 123.997i −389.955 710.884i −3151.46 4245.58i 3404.55i −8814.20 −18067.6
42.4 24.2897i 13.8077i −333.988 427.967i −335.386 2563.83i 1894.31i 6370.35 10395.2
42.5 23.8212i 128.615i −311.450 1187.44i 3063.75 1045.51i 1320.89i −9980.70 28286.2
42.6 23.5327i 46.0777i −297.789 373.886i 1084.33 2487.41i 983.414i 4437.84 −8798.55
42.7 23.0076i 78.5211i −273.350 548.269i −1806.58 2213.93i 399.191i 395.432 −12614.4
42.8 17.7707i 152.462i −59.7986 783.269i 2709.35 1147.99i 3486.64i −16683.5 −13919.3
42.9 14.4463i 49.3343i 47.3041 738.628i −712.698 198.404i 4381.63i 4127.13 10670.5
42.10 11.2266i 77.9859i 129.962 278.075i 875.519 3160.13i 4333.06i 479.207 3121.85
42.11 10.2230i 141.129i 151.490 508.524i −1442.77 610.830i 4165.77i −13356.5 5198.64
42.12 8.15532i 11.7848i 189.491 1153.14i 96.1089 1566.67i 3633.12i 6422.12 −9404.25
42.13 6.19852i 89.9215i 217.578 140.759i 557.380 4216.48i 2935.49i −1524.87 872.500
42.14 5.87436i 114.397i 221.492 623.321i −672.007 2434.57i 2804.96i −6525.57 −3661.61
42.15 5.87436i 114.397i 221.492 623.321i −672.007 2434.57i 2804.96i −6525.57 −3661.61
42.16 6.19852i 89.9215i 217.578 140.759i 557.380 4216.48i 2935.49i −1524.87 872.500
42.17 8.15532i 11.7848i 189.491 1153.14i 96.1089 1566.67i 3633.12i 6422.12 −9404.25
42.18 10.2230i 141.129i 151.490 508.524i −1442.77 610.830i 4165.77i −13356.5 5198.64
42.19 11.2266i 77.9859i 129.962 278.075i 875.519 3160.13i 4333.06i 479.207 3121.85
42.20 14.4463i 49.3343i 47.3041 738.628i −712.698 198.404i 4381.63i 4127.13 10670.5
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 42.28
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
43.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 43.9.b.b 28
43.b odd 2 1 inner 43.9.b.b 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.9.b.b 28 1.a even 1 1 trivial
43.9.b.b 28 43.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{2}^{28} + \cdots\) acting on \(S_{9}^{\mathrm{new}}(43, [\chi])\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database