Properties

Label 43.10.c.a
Level 43
Weight 10
Character orbit 43.c
Analytic conductor 22.147
Analytic rank 0
Dimension 64
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 43 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 43.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(22.1465409550\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 64q - 70q^{2} + 307q^{3} + 16038q^{4} + 681q^{5} - 1281q^{6} + 957q^{7} - 10920q^{8} - 255339q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 64q - 70q^{2} + 307q^{3} + 16038q^{4} + 681q^{5} - 1281q^{6} + 957q^{7} - 10920q^{8} - 255339q^{9} - 6237q^{10} - 180682q^{11} + 274344q^{12} + 115245q^{13} - 171208q^{14} + 138833q^{15} + 4289206q^{16} + 65180q^{17} + 603985q^{18} + 39150q^{19} - 2709775q^{20} - 3105162q^{21} + 598456q^{22} + 1285907q^{23} - 292550q^{24} - 14709917q^{25} + 5332695q^{26} - 20118002q^{27} - 5475298q^{28} + 1274091q^{29} + 28424751q^{30} + 2899781q^{31} - 16322030q^{32} + 30668912q^{33} + 6822099q^{34} - 14750922q^{35} - 113819232q^{36} - 13772217q^{37} + 2700532q^{38} + 49876982q^{39} - 55802359q^{40} + 5375394q^{41} - 62768266q^{42} - 4250879q^{43} - 125171958q^{44} + 74719384q^{45} - 91405220q^{46} + 46104596q^{47} + 294588191q^{48} - 233221733q^{49} + 380339342q^{50} + 229598406q^{51} + 166281612q^{52} + 125396641q^{53} - 137752484q^{54} + 139471854q^{55} + 41104589q^{56} - 289586721q^{57} - 183782516q^{58} - 637949078q^{59} - 70735747q^{60} - 95573327q^{61} + 181277053q^{62} + 226632970q^{63} + 712599660q^{64} - 498753718q^{65} - 349240445q^{66} - 276270786q^{67} + 1034771928q^{68} - 199705103q^{69} + 1780847990q^{70} + 651945247q^{71} - 270063054q^{72} - 182725322q^{73} - 193737672q^{74} - 3155252572q^{75} + 492133584q^{76} + 216024528q^{77} + 2562586420q^{78} - 376932221q^{79} - 783129021q^{80} - 2146956496q^{81} + 2373824428q^{82} + 1008544071q^{83} - 9413139208q^{84} - 1131353054q^{85} - 1641459050q^{86} + 5060470018q^{87} + 369936980q^{88} + 2244184366q^{89} + 3302428348q^{90} + 3951711q^{91} + 4361095637q^{92} + 3133616089q^{93} + 3002217406q^{94} + 1515822931q^{95} + 69408612q^{96} - 6951085934q^{97} + 1120193981q^{98} + 1264470179q^{99} + O(q^{100}) \)

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 −42.7731 124.841 216.230i 1317.54 1213.19 2101.31i −5339.82 + 9248.83i −2678.56 4639.41i −34455.3 −21328.8 36942.6i −51891.8 + 89879.3i
6.2 −42.7383 18.2764 31.6557i 1314.56 −1010.01 + 1749.40i −781.103 + 1352.91i −3156.96 5468.02i −34300.0 9173.44 + 15888.9i 43166.3 74766.2i
6.3 −39.3582 7.60021 13.1640i 1037.06 95.5381 165.477i −299.130 + 518.109i 4791.65 + 8299.38i −20665.6 9725.97 + 16845.9i −3760.20 + 6512.86i
6.4 −38.7934 −85.4891 + 148.071i 992.932 642.710 1113.21i 3316.42 5744.20i −2797.86 4846.03i −18657.0 −4775.28 8271.02i −24932.9 + 43185.1i
6.5 −36.2109 −128.726 + 222.960i 799.229 −873.768 + 1513.41i 4661.28 8073.58i 4633.70 + 8025.80i −10400.8 −23299.2 40355.5i 31639.9 54801.9i
6.6 −31.9531 134.971 233.777i 508.999 −1225.62 + 2122.83i −4312.75 + 7469.90i 3454.19 + 5982.82i 95.8864 −26593.0 46060.4i 39162.2 67830.9i
6.7 −30.5461 46.1090 79.8632i 421.064 286.168 495.658i −1408.45 + 2439.51i 319.069 + 552.644i 2777.74 5589.41 + 9681.15i −8741.33 + 15140.4i
6.8 −26.2732 −64.5490 + 111.802i 178.282 −856.618 + 1483.71i 1695.91 2937.40i −4325.00 7491.12i 8767.84 1508.35 + 2612.53i 22506.1 38981.8i
6.9 −25.7600 66.1575 114.588i 151.580 −107.144 + 185.579i −1704.22 + 2951.80i −2358.57 4085.17i 9284.43 1087.86 + 1884.23i 2760.03 4780.51i
6.10 −25.2231 −62.6577 + 108.526i 124.205 1186.15 2054.47i 1580.42 2737.37i 1704.14 + 2951.66i 9781.39 1989.53 + 3445.96i −29918.4 + 51820.2i
6.11 −17.1502 −66.7974 + 115.697i −217.870 −131.077 + 227.033i 1145.59 1984.22i 1324.62 + 2294.32i 12517.4 917.711 + 1589.52i 2248.01 3893.66i
6.12 −12.6048 108.034 187.120i −353.118 242.203 419.508i −1361.75 + 2358.62i −2218.86 3843.18i 10904.7 −13501.1 23384.6i −3052.92 + 5287.82i
6.13 −11.0082 −0.196357 + 0.340100i −390.819 −1072.23 + 1857.16i 2.16154 3.74389i 3698.39 + 6405.81i 9938.43 9841.42 + 17045.8i 11803.4 20444.0i
6.14 −10.8555 83.9447 145.396i −394.158 1237.61 2143.60i −911.262 + 1578.35i 6087.74 + 10544.3i 9836.80 −4251.92 7364.54i −13434.9 + 23269.9i
6.15 −7.29691 −0.107179 + 0.185640i −458.755 1142.50 1978.86i 0.782078 1.35460i −5889.33 10200.6i 7083.52 9841.48 + 17045.9i −8336.70 + 14439.6i
6.16 −5.60251 −131.864 + 228.395i −480.612 566.701 981.555i 738.770 1279.59i 1382.17 + 2393.98i 5561.12 −24934.8 43188.3i −3174.95 + 5499.17i
6.17 1.79962 −100.854 + 174.685i −508.761 −371.655 + 643.725i −181.499 + 314.366i −4777.62 8275.08i −1836.98 −10501.7 18189.4i −668.837 + 1158.46i
6.18 2.09785 102.202 177.020i −507.599 −192.277 + 333.034i 214.405 371.361i 2053.75 + 3557.19i −2138.97 −11049.2 19137.7i −403.369 + 698.655i
6.19 3.31091 64.4391 111.612i −501.038 −994.242 + 1722.08i 213.352 369.536i −3834.95 6642.33i −3354.07 1536.70 + 2661.64i −3291.84 + 5701.64i
6.20 4.33792 −9.83652 + 17.0374i −493.182 215.967 374.066i −42.6701 + 73.9068i 2230.56 + 3863.44i −4360.41 9647.99 + 16710.8i 936.849 1622.67i
See all 64 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 36.32
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 43.10.c.a 64
43.c even 3 1 inner 43.10.c.a 64
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.10.c.a 64 1.a even 1 1 trivial
43.10.c.a 64 43.c even 3 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{10}^{\mathrm{new}}(43, [\chi])\).

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database