Newform orbit 83.9.b.b

• Label: 83.9.b.b
• Level: $83$
• Weight: $9$
• Character orbit: 83.b
• Analytic conductor: $33.812$
• Analytic rank: $0$
• Dimension: $52$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 83 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	83.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(33.8124246351\)
Analytic rank:	\(0\)
Dimension:	\(52\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 52 q - 114 q^{3} - 8158 q^{4} + 2028 q^{7} + 94094 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
82.1		−	30.8113i	−138.126			−693.333				−	1079.32i			4255.84i	−2443.58					13474.8i	12517.9			−33255.1
82.2		−	29.8646i	−44.3221			−635.894				−	107.844i			1323.66i	3842.40					11345.4i	−4596.55			−3220.73
82.3		−	29.1525i	12.3162			−593.869					216.115i		−	359.048i	−3026.63					9849.71i	−6409.31			6300.28
82.4		−	29.1439i	147.768			−593.367					540.237i		−	4306.54i	−789.238					9832.19i	15274.4			15744.6
82.5		−	28.9183i	−94.3106			−580.269					1005.95i			2727.30i	1267.65					9377.33i	2333.48			29090.4
82.6		−	28.7607i	93.5512			−571.177				−	1011.26i		−	2690.60i	1842.96					9064.71i	2190.82			−29084.5
82.7		−	27.3058i	84.9217			−489.609					452.118i		−	2318.86i	1933.38					6378.89i	650.692			12345.5
82.8		−	24.1555i	−49.1718			−327.490				−	627.474i			1187.77i	533.450					1726.87i	−4143.13			−15157.0
82.9		−	23.1358i	92.5761			−279.265				−	735.829i		−	2141.82i	−3688.47					538.247i	2009.34			−17024.0
82.10		−	22.0230i	−140.300			−229.014					452.091i			3089.84i	−1545.25				−	594.314i	13123.2			9956.42
82.11		−	21.7614i	−54.6769			−217.557				−	215.686i			1189.84i	−1478.12				−	836.577i	−3571.44			−4693.63
82.12		−	20.1432i	38.0182			−149.749					1037.56i		−	765.808i	−807.586				−	2140.23i	−5115.62			20899.7
82.13		−	19.9106i	−119.992			−140.430				−	269.386i			2389.11i	3536.41				−	2301.06i	7837.07			−5363.62
82.14		−	19.7977i	65.2186			−135.948					533.022i		−	1291.18i	3822.00				−	2376.76i	−2307.54			10552.6
82.15		−	18.1346i	10.8010			−72.8619				−	661.511i		−	195.872i	1647.64				−	3321.13i	−6444.34			−11996.2
82.16		−	16.5230i	145.486			−17.0110					69.4678i		−	2403.87i	−435.712				−	3948.83i	14605.1			1147.82
82.17		−	14.8160i	109.440			36.4875				−	648.188i		−	1621.45i	2181.86				−	4333.48i	5416.03			−9603.52
82.18		−	12.7600i	−65.0308			93.1835					769.760i			829.790i	−3342.05				−	4455.57i	−2331.99			9822.10
82.19		−	11.0227i	76.7701			134.500					62.6192i		−	846.216i	−3509.47				−	4304.37i	−667.351			690.235
82.20		−	10.6037i	−70.7011			143.561				−	1098.80i			749.694i	−4491.81				−	4236.83i	−1562.36			−11651.4

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	83.9.b.b	✓	52
83.b	odd	2	1	inner	83.9.b.b	✓	52

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
83.9.b.b	✓	52	1.a	even	1	1	trivial
83.9.b.b	✓	52	83.b	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^52 + 10735*T2^50 + 54147190*T2^48 + 170633480860*T2^46 + 376814206039895*T2^44 + 620001675710588225*T2^42 + 788979710287111644874*T2^40 + 795639476362501242017060*T2^38 + 646359526576523660381612264*T2^36 + 427729203182143034126911144944*T2^34 + 232258801395562072615951556367328*T2^32 + 103938721755473649556080203168871616*T2^30 + 38408514286808093896763406600300910720*T2^28 + 11717827811564340807967604225789408920576*T2^26 + 2945144948580994269901627289946980448034816*T2^24 + 607341545487319785802857843404963877309054976*T2^22 + 102133355064719802996518511754517030068158464000*T2^20 + 13888805186590052056840252453602635720084349255680*T2^18 + 1510453348802344708080877680570490454578505491415040*T2^16 + 129476900393323599026426773703138318565239884097781760*T2^14 + 8582281681643845193217962679720704070326542325619097600*T2^12 + 428632813965364729039642917782259414648907667208771993600*T2^10 + 15550762061135861002285717008373695051241424572368971366400*T2^8 + 387833713660368028820902328377815984347874575158930833408000*T2^6 + 6063796198866120390887921895968537218482845509166850637824000*T2^4 + 49478829362397447122778840145689622522895001839525922078720000*T2^2 + 124337436712570364562508331286605085631598497173212233728000000