Newform orbit 117.3.v.a

• Label: 117.3.v.a
• Level: $117$
• Weight: $3$
• Character orbit: 117.v
• Analytic conductor: $3.188$
• Analytic rank: $0$
• Dimension: $52$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.v (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.18801909302\)
Analytic rank:	\(0\)
Dimension:	\(52\)
Relative dimension:	\(26\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 52 q - 6 q^{2} - q^{3} + 94 q^{4} - 12 q^{6} - 3 q^{7} - 78 q^{8} + q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
95.1	−3.87550			−1.67424	−	2.48936i	11.0195			−2.28307	+	3.95440i	6.48854	+	9.64752i	−6.88777	−	3.97666i	−27.2042			−3.39381	+	8.33559i	8.84806	−	15.3253i
95.2	−3.87182			2.99841	+	0.0975126i	10.9910			4.14167	−	7.17357i	−11.6093	−	0.377552i	1.81522	+	1.04802i	−27.0680			8.98098	+	0.584767i	−16.0358	+	27.7748i
95.3	−3.41734			−0.243983	+	2.99006i	7.67823			−2.84214	+	4.92273i	0.833772	−	10.2181i	9.04095	+	5.21980i	−12.5698			−8.88094	−	1.45905i	9.71257	−	16.8227i
95.4	−3.06335			−2.85400	+	0.924494i	5.38411			1.85161	−	3.20708i	8.74280	−	2.83205i	2.91844	+	1.68496i	−4.24001			7.29062	−	5.27701i	−5.67212	+	9.82439i
95.5	−2.75155			2.71969	+	1.26620i	3.57103			−3.47982	+	6.02723i	−7.48337	−	3.48402i	−8.25359	−	4.76521i	1.18034			5.79347	+	6.88736i	9.57490	−	16.5842i
95.6	−2.74734			1.48534	−	2.60648i	3.54790			−1.55246	+	2.68894i	−4.08075	+	7.16091i	9.10198	+	5.25503i	1.24207			−4.58751	−	7.74305i	4.26515	−	7.38745i
95.7	−2.43163			0.199346	+	2.99337i	1.91280			3.20934	−	5.55874i	−0.484736	−	7.27875i	−6.20094	−	3.58011i	5.07529			−8.92052	+	1.19343i	−7.80391	+	13.5168i
95.8	−2.20869			−0.799724	−	2.89144i	0.878318			3.11152	−	5.38931i	1.76634	+	6.38631i	−2.77300	−	1.60099i	6.89483			−7.72088	+	4.62471i	−6.87238	+	11.9033i
95.9	−1.89224			−2.97271	+	0.403710i	−0.419442			−2.45061	+	4.24459i	5.62507	−	0.763915i	−5.47305	−	3.15987i	8.36263			8.67404	−	2.40023i	4.63714	−	8.03176i
95.10	−1.24178			2.92556	+	0.664154i	−2.45799			0.320482	−	0.555091i	−3.63289	−	0.824730i	4.77079	+	2.75441i	8.01938			8.11780	+	3.88604i	−0.397967	+	0.689299i
95.11	−0.647795			−2.17539	−	2.06583i	−3.58036			−1.12097	+	1.94158i	1.40921	+	1.33823i	6.66709	+	3.84925i	4.91052			0.464681	+	8.98800i	0.726158	−	1.25774i
95.12	−0.479501			0.165651	+	2.99542i	−3.77008			−0.131616	+	0.227965i	−0.0794300	−	1.43631i	0.478346	+	0.276173i	3.72576			−8.94512	+	0.992391i	0.0631100	−	0.109310i
95.13	−0.276632			2.49716	−	1.66258i	−3.92347			2.47988	−	4.29528i	−0.690795	+	0.459924i	−5.93519	−	3.42668i	2.19189			3.47164	−	8.30348i	−0.686015	+	1.18821i
95.14	0.000488132	0		1.05456	−	2.80854i	−4.00000			−4.59055	+	7.95106i	0.000514765	−	0.00137094i	−4.99500	−	2.88386i	−0.00390505			−6.77580	−	5.92356i	−0.00224079	+	0.00388116i
95.15	0.240822			−2.46946	+	1.70345i	−3.94200			4.12967	−	7.15280i	−0.594701	+	0.410228i	9.43694	+	5.44842i	−1.91261			3.19651	−	8.41322i	0.994515	−	1.72255i
95.16	1.17583			−2.06653	+	2.17473i	−2.61741			−0.331589	+	0.574329i	−2.42990	+	2.55712i	−10.7993	−	6.23496i	−7.78098			−0.458901	−	8.98829i	−0.389894	+	0.675315i
95.17	1.18838			1.78897	+	2.40823i	−2.58776			−3.27957	+	5.68038i	2.12597	+	2.86189i	2.09412	+	1.20904i	−7.82874			−2.59915	+	8.61652i	−3.89736	+	6.75042i
95.18	1.34192			−2.64219	−	1.42085i	−2.19924			0.383399	−	0.664067i	−3.54562	−	1.90667i	−4.75014	−	2.74250i	−8.31891			4.96237	+	7.50832i	0.514492	−	0.891127i
95.19	1.85429			−0.157122	−	2.99588i	−0.561614			2.88924	−	5.00431i	−0.291350	−	5.55523i	−2.01841	−	1.16533i	−8.45855			−8.95063	+	0.941440i	5.35749	−	9.27944i
95.20	2.03688			2.68285	−	1.34250i	0.148870			0.0620677	−	0.107504i	5.46464	−	2.73451i	7.73476	+	4.46566i	−7.84428			5.39539	−	7.20346i	0.126424	−	0.218973i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
117.v	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	117.3.v.a	yes	52
3.b	odd	2	1		351.3.v.a		52
9.c	even	3	1		351.3.m.a		52
9.d	odd	6	1		117.3.m.a	✓	52
13.e	even	6	1		117.3.m.a	✓	52
39.h	odd	6	1		351.3.m.a		52
117.l	even	6	1		351.3.v.a		52
117.v	odd	6	1	inner	117.3.v.a	yes	52

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
117.3.m.a	✓	52	9.d	odd	6	1
117.3.m.a	✓	52	13.e	even	6	1
117.3.v.a	yes	52	1.a	even	1	1	trivial
117.3.v.a	yes	52	117.v	odd	6	1	inner
351.3.m.a		52	9.c	even	3	1
351.3.m.a		52	39.h	odd	6	1
351.3.v.a		52	3.b	odd	2	1
351.3.v.a		52	117.l	even	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(117, [\chi])\).