Properties

Label 43.7.d.a
Level 43
Weight 7
Character orbit 43.d
Analytic conductor 9.892
Analytic rank 0
Dimension 42
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 43.d (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.89232559565\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(21\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 42q - 3q^{3} - 1194q^{4} - 3q^{5} + 111q^{6} - 147q^{7} + 3852q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 42q - 3q^{3} - 1194q^{4} - 3q^{5} + 111q^{6} - 147q^{7} + 3852q^{9} - 981q^{10} - 4104q^{11} + 918q^{12} + 4843q^{13} + 2814q^{14} - 163q^{15} + 36678q^{16} + 3641q^{17} - 507q^{18} - 5229q^{19} - 1599q^{20} - 29990q^{21} + 6575q^{23} - 4622q^{24} + 68484q^{25} + 189q^{26} + 48948q^{28} + 95361q^{29} - 85041q^{30} - 79373q^{31} - 79638q^{33} - 184743q^{34} - 80582q^{35} + 59972q^{36} - 66063q^{37} - 69820q^{38} + 189951q^{40} + 40632q^{41} - 368728q^{43} + 130330q^{44} + 34056q^{46} - 247820q^{47} + 326907q^{48} - 21876q^{49} - 28638q^{50} - 617150q^{52} + 11639q^{53} + 655904q^{54} - 43638q^{55} + 553875q^{56} - 422859q^{57} + 587796q^{58} - 649352q^{59} + 875455q^{60} - 52251q^{61} + 1335249q^{62} + 93690q^{63} - 792420q^{64} + 160395q^{66} - 173603q^{67} + 22286q^{68} + 870417q^{69} + 1670505q^{71} - 2068518q^{72} - 2646201q^{73} - 1625030q^{74} - 80622q^{76} - 486066q^{77} + 2835040q^{78} + 1897639q^{79} - 817059q^{80} + 2215367q^{81} + 1584059q^{83} - 824560q^{84} - 2333682q^{86} - 5547198q^{87} + 2736939q^{89} + 1092196q^{90} - 3724131q^{91} + 470257q^{92} + 488433q^{93} - 1289839q^{95} + 1697650q^{96} + 5260848q^{97} + 4722621q^{98} + 1375834q^{99} + O(q^{100}) \)

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 15.1507i 15.3614 8.86889i −165.545 63.9718 36.9341i −134.370 232.736i −298.109 172.114i 1538.48i −207.186 + 358.856i −559.579 969.219i
7.2 13.4327i −34.2137 + 19.7533i −116.436 −28.7813 + 16.6169i 265.339 + 459.580i −186.356 107.593i 704.357i 415.884 720.332i 223.209 + 386.609i
7.3 12.4749i 3.88212 2.24134i −91.6224 −151.098 + 87.2364i −27.9605 48.4289i 378.610 + 218.590i 344.585i −354.453 + 613.930i 1088.26 + 1884.93i
7.4 10.6207i −24.0449 + 13.8823i −48.8003 200.632 115.835i 147.441 + 255.375i 396.423 + 228.875i 161.432i 20.9373 36.2644i −1230.26 2130.86i
7.5 10.1559i 30.5813 17.6561i −39.1423 101.658 58.6923i −179.314 310.581i 191.878 + 110.781i 252.452i 258.977 448.562i −596.073 1032.43i
7.6 7.84004i 36.4833 21.0637i 2.53376 −116.673 + 67.3609i −165.140 286.031i −385.031 222.298i 521.627i 522.856 905.613i 528.113 + 914.718i
7.7 6.95456i −14.3583 + 8.28978i 15.6341 9.86801 5.69730i 57.6517 + 99.8557i −310.875 179.484i 553.820i −227.059 + 393.278i −39.6222 68.6277i
7.8 4.28699i −41.9299 + 24.2082i 45.6217 −171.014 + 98.7351i 103.780 + 179.753i 223.732 + 129.172i 469.947i 807.577 1398.76i 423.276 + 733.136i
7.9 2.64495i −0.554504 + 0.320143i 57.0043 14.6929 8.48295i 0.846761 + 1.46663i 131.768 + 76.0760i 320.050i −364.295 + 630.977i −22.4370 38.8619i
7.10 0.178867i 33.4310 19.3014i 63.9680 21.1050 12.1850i −3.45239 5.97972i 409.144 + 236.219i 22.8893i 380.590 659.200i −2.17950 3.77500i
7.11 1.51738i 20.0424 11.5715i 61.6975 211.318 122.005i 17.5584 + 30.4120i −447.414 258.315i 190.731i −96.7022 + 167.493i 185.128 + 320.651i
7.12 1.95704i 10.4424 6.02890i 60.1700 −193.167 + 111.525i 11.7988 + 20.4361i −30.2778 17.4809i 243.006i −291.805 + 505.421i −218.259 378.036i
7.13 2.61500i −35.7187 + 20.6222i 57.1618 121.716 70.2726i −53.9270 93.4043i 140.639 + 81.1978i 316.838i 486.049 841.861i 183.763 + 318.286i
7.14 6.20332i −29.5720 + 17.0734i 25.5189 −46.5574 + 26.8799i −105.912 183.445i −448.906 259.176i 555.314i 218.503 378.459i −166.745 288.810i
7.15 7.38637i −8.75832 + 5.05662i 9.44147 10.2848 5.93793i −37.3501 64.6923i 367.060 + 211.922i 542.466i −313.361 + 542.757i 43.8598 + 75.9673i
7.16 8.15234i 41.5767 24.0043i −2.46071 −26.4676 + 15.2811i 195.692 + 338.948i 6.27128 + 3.62073i 501.689i 787.917 1364.71i −124.577 215.773i
7.17 9.90547i 12.0709 6.96915i −34.1183 −41.4735 + 23.9447i 69.0327 + 119.568i −415.762 240.040i 295.992i −267.362 + 463.084i −237.184 410.814i
7.18 12.2048i 14.4234 8.32735i −84.9566 131.217 75.7580i 101.633 + 176.034i 221.781 + 128.045i 255.771i −225.811 + 391.115i 924.609 + 1601.47i
7.19 12.8196i −27.1856 + 15.6956i −100.343 −154.521 + 89.2129i −201.212 348.509i 237.672 + 137.220i 465.907i 128.203 222.054i −1143.68 1980.91i
7.20 14.0830i −28.7233 + 16.5834i −134.330 147.495 85.1564i −233.544 404.510i −245.226 141.581i 990.457i 185.520 321.330i 1199.26 + 2077.17i
See all 42 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 37.21
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 43.7.d.a 42
43.d odd 6 1 inner 43.7.d.a 42
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.7.d.a 42 1.a even 1 1 trivial
43.7.d.a 42 43.d odd 6 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{7}^{\mathrm{new}}(43, [\chi])\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database