Newform orbit 61.8.b.a

• Label: 61.8.b.a
• Level: $61$
• Weight: $8$
• Character orbit: 61.b
• Analytic conductor: $19.055$
• Analytic rank: $0$
• Dimension: $34$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	61.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(19.0554865545\)
Analytic rank:	\(0\)
Dimension:	\(34\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 34 q + 52 q^{3} - 1974 q^{4} + 696 q^{5} + 18902 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
60.1		−	21.1768i	5.12910			−320.455			−325.462				−	108.618i			213.497i			4075.57i	−2160.69					6892.23i
60.2		−	19.7034i	−62.9530			−260.223			−118.634					1240.39i			67.8399i			2605.25i	1776.08					2337.49i
60.3		−	19.6906i	−11.3262			−259.721			547.423					223.020i		−	1201.92i			2593.68i	−2058.72				−	10779.1i
60.4		−	19.6035i	83.9512			−256.299			90.0815				−	1645.74i		−	528.783i			2515.11i	4860.80				−	1765.92i
60.5		−	19.5872i	32.3242			−255.657			177.514				−	633.139i			1329.07i			2500.43i	−1142.15				−	3477.00i
60.6		−	15.0747i	−81.9260			−99.2480			263.133					1235.01i			570.938i		−	433.430i	4524.86				−	3966.67i
60.7		−	14.4645i	−26.7067			−81.2226			−66.2560					386.300i		−	1491.78i		−	676.613i	−1473.75					958.362i
60.8		−	14.4421i	49.0072			−80.5732			−358.980				−	707.765i		−	528.378i		−	684.941i	214.706					5184.41i
60.9		−	12.1805i	−9.04702			−20.3636			140.613					110.197i			1136.97i		−	1311.06i	−2105.15				−	1712.73i
60.10		−	11.9218i	44.5664			−14.1287			221.752				−	531.311i			241.796i		−	1357.55i	−200.837				−	2643.68i
60.11		−	9.62716i	−43.0707			35.3178			−487.019					414.649i			870.564i		−	1572.29i	−331.912					4688.61i
60.12		−	6.31212i	60.6173			88.1572			374.242				−	382.623i		−	817.890i		−	1364.41i	1487.46				−	2362.26i
60.13		−	6.16540i	87.9743			89.9879			−212.544				−	542.396i			1694.83i		−	1343.98i	5552.48					1310.42i
60.14		−	5.47002i	−46.6549			98.0789			442.164					255.203i			480.968i		−	1236.66i	−10.3159				−	2418.65i
60.15		−	4.97425i	−77.4209			103.257			−105.514					385.111i		−	1019.04i		−	1150.33i	3807.00					524.852i
60.16		−	3.06899i	−9.88688			118.581			42.5419					30.3427i		−	961.164i		−	756.755i	−2089.25				−	130.561i
60.17		−	0.698820i	31.4227			127.512			−277.058				−	21.9588i		−	565.293i		−	178.557i	−1199.61					193.614i
60.18			0.698820i	31.4227			127.512			−277.058					21.9588i			565.293i			178.557i	−1199.61				−	193.614i
60.19			3.06899i	−9.88688			118.581			42.5419				−	30.3427i			961.164i			756.755i	−2089.25					130.561i
60.20			4.97425i	−77.4209			103.257			−105.514				−	385.111i			1019.04i			1150.33i	3807.00				−	524.852i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	61.8.b.a	✓	34
61.b	even	2	1	inner	61.8.b.a	✓	34

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
61.8.b.a	✓	34	1.a	even	1	1	trivial
61.8.b.a	✓	34	61.b	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{8}^{\mathrm{new}}(61, [\chi])\).