Properties

Label 43.6.g.a
Level 43
Weight 6
Character orbit 43.g
Analytic conductor 6.897
Analytic rank 0
Dimension 204
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 43.g (of order \(21\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89650425196\)
Analytic rank: \(0\)
Dimension: \(204\)
Relative dimension: \(17\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 204q - 468q^{4} - 85q^{5} - 22q^{6} + 454q^{7} + 698q^{8} - 333q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 204q - 468q^{4} - 85q^{5} - 22q^{6} + 454q^{7} + 698q^{8} - 333q^{9} + 303q^{10} - 1340q^{11} + 858q^{12} + 814q^{13} + 1202q^{14} - 2083q^{15} - 6248q^{16} - 214q^{17} - 174q^{18} - 246q^{19} - 17139q^{20} + 3007q^{21} + 2118q^{22} + 3192q^{23} + 15880q^{24} + 3652q^{25} - 1237q^{26} + 108q^{27} - 6780q^{28} - 18827q^{29} + 98080q^{30} - 43196q^{31} - 3930q^{32} + 28181q^{33} + 45155q^{34} + 33275q^{35} - 49399q^{36} + 34607q^{37} - 43374q^{38} + 15155q^{39} - 108727q^{40} + 7156q^{41} - 48066q^{42} - 176452q^{43} + 26068q^{44} - 96386q^{45} - 27185q^{46} + 20402q^{47} + 198899q^{48} - 158742q^{49} + 186243q^{50} + 98589q^{51} + 278918q^{52} + 14102q^{53} + 270894q^{54} - 334770q^{55} + 61999q^{56} - 202490q^{57} + 213658q^{58} - 43753q^{59} - 389005q^{60} + 80516q^{61} + 162349q^{62} - 75177q^{63} - 489850q^{64} + 93726q^{65} + 246095q^{66} - 322922q^{67} + 475089q^{68} - 397079q^{69} - 614985q^{70} - 233345q^{71} + 379655q^{72} + 159391q^{73} + 695938q^{74} + 344081q^{75} - 50808q^{76} + 608177q^{77} + 605548q^{78} - 272109q^{79} + 601054q^{80} + 193536q^{81} - 996896q^{82} + 177813q^{83} - 919009q^{84} - 844524q^{85} - 876752q^{86} - 188214q^{87} - 59998q^{88} - 469041q^{89} - 453431q^{90} - 223189q^{91} - 94922q^{92} + 569174q^{93} + 1175168q^{94} + 435689q^{95} + 1557688q^{96} + 643751q^{97} + 886196q^{98} + 1422581q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
9.1 −6.52161 8.17784i 17.3296 + 2.61202i −17.2250 + 75.4676i 2.46584 + 1.68118i −91.6562 158.753i 94.8911 164.356i 427.928 206.079i 61.2883 + 18.9049i −2.33281 31.1292i
9.2 −5.80705 7.28181i −18.0713 2.72380i −12.1822 + 53.3739i −87.0006 59.3160i 85.1064 + 147.409i −25.6945 + 44.5042i 190.876 91.9209i 86.9470 + 26.8196i 73.2889 + 977.972i
9.3 −5.47096 6.86037i −18.4151 2.77564i −10.0126 + 43.8679i 64.4216 + 43.9219i 81.7066 + 141.520i 8.11387 14.0536i 102.744 49.4787i 99.2091 + 30.6020i −51.1277 682.251i
9.4 −5.14921 6.45690i 12.1966 + 1.83835i −8.05656 + 35.2981i 6.56775 + 4.47782i −50.9330 88.2185i −125.151 + 216.768i 31.2951 15.0709i −86.8258 26.7822i −4.90589 65.4645i
9.5 −3.60873 4.52520i −0.0525050 0.00791386i −0.333852 + 1.46270i −19.3143 13.1682i 0.153664 + 0.266155i 53.2202 92.1801i −159.048 + 76.5937i −232.201 71.6247i 10.1110 + 134.921i
9.6 −2.33890 2.93289i 28.6156 + 4.31311i 3.98929 17.4782i −77.5461 52.8700i −54.2792 94.0143i 35.5619 61.5951i −168.746 + 81.2638i 568.046 + 175.219i 26.3107 + 351.092i
9.7 −1.80763 2.26670i 21.5746 + 3.25185i 5.25028 23.0030i 62.1654 + 42.3837i −31.6280 54.7813i 1.33082 2.30504i −145.219 + 69.9337i 222.685 + 68.6892i −16.3012 217.525i
9.8 −1.23023 1.54266i −24.9627 3.76252i 6.25434 27.4020i −22.2688 15.1826i 24.9055 + 43.1377i −4.12718 + 7.14849i −106.854 + 51.4581i 376.774 + 116.219i 3.97415 + 53.0313i
9.9 −1.10270 1.38274i −5.76893 0.869526i 6.42464 28.1482i 43.6641 + 29.7697i 5.15906 + 8.93576i 20.6505 35.7677i −96.9964 + 46.7110i −199.680 61.5931i −6.98461 93.2031i
9.10 0.425286 + 0.533292i 2.86518 + 0.431857i 7.01714 30.7441i −54.5646 37.2015i 0.988217 + 1.71164i −110.445 + 191.296i 39.0457 18.8034i −224.181 69.1508i −3.36630 44.9201i
9.11 2.53765 + 3.18211i 2.05098 + 0.309135i 3.43451 15.0476i −53.1952 36.2679i 4.22095 + 7.31090i 95.1032 164.724i 173.943 83.7664i −228.093 70.3575i −19.5823 261.308i
9.12 2.59848 + 3.25839i 17.4103 + 2.62418i 3.25566 14.2640i 30.9820 + 21.1232i 36.6897 + 63.5485i 16.4293 28.4563i 175.095 84.3211i 64.0287 + 19.7502i 11.6786 + 155.840i
9.13 2.92560 + 3.66858i −13.3552 2.01297i 2.22129 9.73211i 69.6328 + 47.4749i −31.6872 54.8838i −99.9777 + 173.166i 177.485 85.4723i −57.8948 17.8582i 29.5522 + 394.346i
9.14 3.93041 + 4.92858i −23.5623 3.55144i −1.72210 + 7.54503i 6.81244 + 4.64464i −75.1059 130.087i 57.5727 99.7189i 137.793 66.3574i 310.364 + 95.7346i 3.88420 + 51.8310i
9.15 5.30682 + 6.65454i 23.7101 + 3.57372i −8.99992 + 39.4312i −24.4442 16.6658i 102.044 + 176.745i −48.7498 + 84.4371i −64.7633 + 31.1883i 317.192 + 97.8407i −18.8179 251.108i
9.16 5.80897 + 7.28422i −11.9998 1.80868i −12.1950 + 53.4298i −56.0782 38.2335i −56.5318 97.9160i −58.6801 + 101.637i −191.420 + 92.1833i −91.4795 28.2177i −47.2556 630.582i
9.17 6.32555 + 7.93199i 2.21950 + 0.334535i −15.7832 + 69.1506i 53.6893 + 36.6047i 11.3860 + 19.7211i 51.6195 89.4076i −355.837 + 171.362i −227.390 70.1405i 49.2659 + 657.407i
10.1 −2.36214 10.3492i −5.75023 5.33543i −72.6953 + 35.0082i −7.82578 + 1.17955i −41.6347 + 72.1133i 62.4925 + 108.240i 322.229 + 404.063i −13.5611 180.961i 30.6929 + 78.2043i
10.2 −2.02425 8.86884i 20.8925 + 19.3854i −45.7276 + 22.0213i −27.6125 + 4.16191i 129.634 224.533i 100.934 + 174.822i 106.369 + 133.382i 42.5431 + 567.698i 92.8059 + 236.466i
10.3 −1.91263 8.37977i 7.67423 + 7.12065i −37.7314 + 18.1705i 59.1521 8.91575i 44.9914 77.9274i −90.2330 156.288i 52.9405 + 66.3853i −9.96919 133.030i −187.848 478.629i
See next 80 embeddings (of 204 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 40.17
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
43.g even 21 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 43.6.g.a 204
43.g even 21 1 inner 43.6.g.a 204
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.6.g.a 204 1.a even 1 1 trivial
43.6.g.a 204 43.g even 21 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{6}^{\mathrm{new}}(43, [\chi])\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database