Properties

Label 43.6.c.a
Level 43
Weight 6
Character orbit 43.c
Analytic conductor 6.897
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 43 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 43.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89650425196\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 34q - 14q^{2} - 14q^{3} + 454q^{4} + 71q^{5} + 15q^{6} + 225q^{7} - 936q^{8} - 1011q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 34q - 14q^{2} - 14q^{3} + 454q^{4} + 71q^{5} + 15q^{6} + 225q^{7} - 936q^{8} - 1011q^{9} - 317q^{10} + 1326q^{11} - 648q^{12} + 1006q^{13} - 1272q^{14} + 683q^{15} + 3574q^{16} + 200q^{17} + 1861q^{18} + 3361q^{19} + 3825q^{20} - 1320q^{21} - 8768q^{22} + 560q^{23} - 7382q^{24} - 3232q^{25} - 3201q^{26} - 122q^{27} + 13934q^{28} + 8887q^{29} - 19449q^{30} - 6749q^{31} - 19086q^{32} + 7106q^{33} + 8423q^{34} + 31118q^{35} - 14112q^{36} - 4514q^{37} + 7072q^{38} - 5404q^{39} - 18519q^{40} - 28996q^{41} + 58118q^{42} - 14998q^{43} + 71050q^{44} - 92096q^{45} + 20052q^{46} - 10742q^{47} + 32927q^{48} + 7472q^{49} + 20362q^{50} + 20250q^{51} + 59532q^{52} - 50572q^{53} - 230084q^{54} + 38544q^{55} - 40355q^{56} - 18087q^{57} - 33436q^{58} + 112654q^{59} + 134093q^{60} - 20120q^{61} - 31491q^{62} + 188227q^{63} + 125164q^{64} - 36578q^{65} + 8803q^{66} - 73824q^{67} - 128456q^{68} + 8005q^{69} - 141610q^{70} + 142842q^{71} + 98466q^{72} - 91624q^{73} - 99720q^{74} + 298358q^{75} + 258288q^{76} + 68051q^{77} - 201116q^{78} + 99734q^{79} - 31261q^{80} - 28441q^{81} - 147772q^{82} - 47340q^{83} - 624232q^{84} - 71734q^{85} - 115526q^{86} - 215924q^{87} - 720684q^{88} + 60402q^{89} + 676108q^{90} + 164172q^{91} + 78997q^{92} - 40793q^{93} - 341874q^{94} + 123541q^{95} - 442140q^{96} + 318476q^{97} + 217473q^{98} - 134770q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
6.1 −10.9797 8.65096 14.9839i 88.5548 −5.02316 + 8.70037i −94.9853 + 164.519i 36.4175 + 63.0770i −620.957 −28.1782 48.8060i 55.1531 95.5279i
6.2 −9.23558 −13.7527 + 23.8204i 53.2959 45.8176 79.3585i 127.015 219.996i 101.216 + 175.312i −196.680 −256.776 444.749i −423.152 + 732.921i
6.3 −8.55067 −3.32584 + 5.76053i 41.1139 8.72223 15.1073i 28.4382 49.2563i −112.908 195.562i −77.9301 99.3776 + 172.127i −74.5809 + 129.178i
6.4 −8.35737 −3.42253 + 5.92800i 37.8456 −28.3920 + 49.1763i 28.6033 49.5425i 46.8510 + 81.1483i −48.8539 98.0726 + 169.867i 237.282 410.985i
6.5 −6.28648 10.0721 17.4453i 7.51978 38.9844 67.5229i −63.3177 + 109.670i 4.83274 + 8.37056i 153.894 −81.3925 140.976i −245.074 + 424.481i
6.6 −4.45148 9.81167 16.9943i −12.1844 −39.8809 + 69.0757i −43.6764 + 75.6497i 8.78791 + 15.2211i 196.686 −71.0376 123.041i 177.529 307.489i
6.7 −3.30883 −12.3585 + 21.4055i −21.0516 −32.1287 + 55.6486i 40.8922 70.8273i −2.83477 4.90997i 175.539 −183.964 318.635i 106.309 184.132i
6.8 −2.35784 −4.70904 + 8.15629i −26.4406 15.5528 26.9382i 11.1032 19.2313i −36.1175 62.5573i 137.794 77.1499 + 133.628i −36.6710 + 63.5160i
6.9 −1.24721 −0.494517 + 0.856528i −30.4445 24.3642 42.2000i 0.616768 1.06827i 83.1429 + 144.008i 77.8815 121.011 + 209.597i −30.3873 + 52.6324i
6.10 1.74361 7.37567 12.7750i −28.9598 −8.29752 + 14.3717i 12.8603 22.2747i −98.7307 171.007i −106.290 12.6989 + 21.9952i −14.4677 + 25.0587i
6.11 3.69441 −11.8232 + 20.4784i −18.3513 21.7696 37.7061i −43.6798 + 75.6556i −19.0405 32.9792i −186.018 −158.077 273.797i 80.4259 139.302i
6.12 4.36550 0.424863 0.735884i −12.9424 −30.5339 + 52.8863i 1.85474 3.21250i 93.7016 + 162.296i −196.196 121.139 + 209.819i −133.296 + 230.875i
6.13 4.50187 14.9934 25.9693i −11.7331 16.1936 28.0482i 67.4982 116.910i 70.7811 + 122.596i −196.881 −328.101 568.288i 72.9017 126.269i
6.14 6.70145 −7.23861 + 12.5376i 12.9095 −40.0400 + 69.3513i −48.5092 + 84.0205i −74.8208 129.593i −127.934 16.7049 + 28.9338i −268.326 + 464.754i
6.15 7.09985 1.12246 1.94417i 18.4079 51.2710 88.8039i 7.96933 13.8033i −36.3371 62.9377i −96.5019 118.980 + 206.080i 364.016 630.495i
6.16 9.70119 7.50728 13.0030i 62.1131 −9.53861 + 16.5214i 72.8296 126.145i −13.4501 23.2962i 292.133 8.78143 + 15.2099i −92.5359 + 160.277i
6.17 9.96731 −9.83333 + 17.0318i 67.3472 6.65929 11.5342i −98.0118 + 169.761i 61.0081 + 105.669i 352.316 −71.8888 124.515i 66.3751 114.965i
36.1 −10.9797 8.65096 + 14.9839i 88.5548 −5.02316 8.70037i −94.9853 164.519i 36.4175 63.0770i −620.957 −28.1782 + 48.8060i 55.1531 + 95.5279i
36.2 −9.23558 −13.7527 23.8204i 53.2959 45.8176 + 79.3585i 127.015 + 219.996i 101.216 175.312i −196.680 −256.776 + 444.749i −423.152 732.921i
36.3 −8.55067 −3.32584 5.76053i 41.1139 8.72223 + 15.1073i 28.4382 + 49.2563i −112.908 + 195.562i −77.9301 99.3776 172.127i −74.5809 129.178i
See all 34 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 36.17
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
43.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 43.6.c.a 34
43.c even 3 1 inner 43.6.c.a 34
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.6.c.a 34 1.a even 1 1 trivial
43.6.c.a 34 43.c even 3 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