Newform orbit 109.6.b.a

• Label: 109.6.b.a
• Level: $109$
• Weight: $6$
• Character orbit: 109.b
• Analytic conductor: $17.482$
• Analytic rank: $0$
• Dimension: $46$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 109 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	109.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(17.4818363596\)
Analytic rank:	\(0\)
Dimension:	\(46\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 46 q + 16 q^{3} - 768 q^{4} - 50 q^{5} + 2 q^{7} + 3286 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
108.1		−	10.8188i	6.27735			−85.0469			−56.3486				−	67.9135i	209.547					573.905i	−203.595					609.626i
108.2		−	10.3864i	13.1977			−75.8764			8.75949				−	137.076i	−134.228					455.715i	−68.8196				−	90.9792i
108.3		−	10.3259i	−17.2980			−74.6237			−4.57612					178.617i	−197.588					440.127i	56.2219					47.2525i
108.4		−	10.1221i	−2.75303			−70.4570			102.236					27.8665i	119.565					389.266i	−235.421				−	1034.84i
108.5		−	9.52583i	−27.0868			−58.7414			−0.336174					258.024i	124.503					254.734i	490.693					3.20234i
108.6		−	9.29066i	30.0807			−54.3164			56.5138				−	279.470i	37.4837					207.334i	661.851				−	525.051i
108.7		−	8.86822i	−12.5201			−46.6453			−104.214					111.031i	−57.2950					129.877i	−86.2478					924.195i
108.8		−	8.79838i	15.0622			−45.4115			−29.8961				−	132.523i	−84.5486					117.999i	−16.1287					263.037i
108.9		−	7.71396i	−10.2232			−27.5052			72.8801					78.8614i	−106.884				−	34.6726i	−138.486				−	562.195i
108.10		−	7.18485i	11.7060			−19.6221			11.0126				−	84.1059i	−16.3055				−	88.9333i	−105.970				−	79.1236i
108.11		−	6.97267i	26.3194			−16.6181			−92.3335				−	183.516i	188.472				−	107.253i	449.709					643.811i
108.12		−	6.75749i	−12.6149			−13.6636			8.11472					85.2447i	155.938				−	123.908i	−83.8656				−	54.8351i
108.13		−	5.81174i	−4.22237			−1.77635			−48.9433					24.5393i	50.4778				−	175.652i	−225.172					284.446i
108.14		−	4.95182i	−28.2518			7.47951			57.6222					139.898i	−113.886				−	195.495i	555.162				−	285.334i
108.15		−	4.90427i	19.5501			7.94809			−78.9682				−	95.8789i	−226.487				−	195.916i	139.205					387.281i
108.16		−	4.38905i	17.4177			12.7362			111.333				−	76.4471i	−151.359				−	196.350i	60.3759				−	488.646i
108.17		−	4.18676i	13.3939			14.4711			53.0126				−	56.0770i	197.518				−	194.563i	−63.6036				−	221.951i
108.18		−	3.63231i	−19.9726			18.8063			−62.9116					72.5467i	−167.781				−	184.544i	155.904					228.515i
108.19		−	2.52254i	−24.4350			25.6368			−51.2905					61.6381i	135.118				−	145.391i	354.067					129.382i
108.20		−	2.25353i	−1.56271			26.9216			21.0691					3.52161i	−142.573				−	132.782i	−240.558				−	47.4798i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	109.6.b.a	✓	46
109.b	even	2	1	inner	109.6.b.a	✓	46

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
109.6.b.a	✓	46	1.a	even	1	1	trivial
109.6.b.a	✓	46	109.b	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{6}^{\mathrm{new}}(109, [\chi])\).