Newform orbit 671.2.o.a

• Label: 671.2.o.a
• Level: $671$
• Weight: $2$
• Character orbit: 671.o
• Analytic conductor: $5.358$
• Analytic rank: $0$
• Dimension: $100$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.35796197563\)
Analytic rank:	\(0\)
Dimension:	\(100\)
Relative dimension:	\(50\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 100 q + 4 q^{3} + 38 q^{4} - 6 q^{5} + 12 q^{6} + 6 q^{7} + 96 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
353.1	−2.28333	−	1.31828i	−2.61743			2.47573	+	4.28809i	0.483876	−	0.838098i	5.97645	+	3.45051i	−2.89686	−	1.67250i		−	7.78170i	3.85093			−2.20970	+	1.27577i
353.2	−2.25208	−	1.30024i	−1.39379			2.38123	+	4.12442i	−1.39465	+	2.41560i	3.13893	+	1.81226i	2.34580	+	1.35435i		−	7.18372i	−1.05734			6.28170	−	3.62674i
353.3	−2.16485	−	1.24988i	−0.750612			2.12440	+	3.67956i	1.39042	−	2.40828i	1.62496	+	0.938174i	1.80357	+	1.04129i		−	5.62144i	−2.43658			−6.02013	+	3.47572i
353.4	−2.04058	−	1.17813i	1.10807			1.77599	+	3.07611i	−0.773884	+	1.34041i	−2.26110	−	1.30545i	2.33677	+	1.34914i		−	3.65688i	−1.77219			3.15835	−	1.82348i
353.5	−1.95214	−	1.12707i	3.30065			1.54058	+	2.66836i	−1.38341	+	2.39614i	−6.44334	−	3.72006i	2.30926	+	1.33325i		−	2.43708i	7.89427			5.40124	−	3.11841i
353.6	−1.94485	−	1.12286i	2.13240			1.52163	+	2.63554i	−1.62555	+	2.81554i	−4.14721	−	2.39439i	−3.97334	−	2.29401i		−	2.34287i	1.54715			6.32292	−	3.65054i
353.7	−1.93983	−	1.11996i	−0.234803			1.50863	+	2.61302i	0.0821411	−	0.142272i	0.455478	+	0.262970i	−2.78442	−	1.60758i		−	2.27859i	−2.94487			−0.318680	+	0.183990i
353.8	−1.81114	−	1.04566i	−2.97181			1.18683	+	2.05564i	−1.33911	+	2.31941i	5.38237	+	3.10751i	3.08940	+	1.78367i		−	0.781432i	5.83165			4.85066	−	2.80053i
353.9	−1.66014	−	0.958485i	−2.72985			0.837387	+	1.45040i	1.58254	−	2.74105i	4.53195	+	2.61652i	2.39252	+	1.38132i			0.623448i	4.45211			−5.25450	+	3.03369i
353.10	−1.61255	−	0.931003i	2.83991			0.733534	+	1.27052i	1.48075	−	2.56473i	−4.57948	−	2.64396i	−1.11196	−	0.641989i			0.992322i	5.06507			−4.77554	+	2.75716i
353.11	−1.50557	−	0.869242i	0.472199			0.511163	+	0.885361i	−0.131210	+	0.227263i	−0.710929	−	0.410455i	3.18489	+	1.83880i			1.69967i	−2.77703			0.395093	−	0.228107i
353.12	−1.48575	−	0.857801i	1.46323			0.471645	+	0.816913i	0.492748	−	0.853464i	−2.17399	−	1.25516i	−2.66588	−	1.53914i			1.81289i	−0.858970			−1.46420	+	0.845359i
353.13	−1.47682	−	0.852642i	−1.17833			0.453995	+	0.786343i	−0.185718	+	0.321673i	1.74018	+	1.00469i	0.148482	+	0.0857259i			1.86218i	−1.61154			0.548544	−	0.316702i
353.14	−1.27894	−	0.738395i	−2.99796			0.0904543	+	0.156671i	0.951983	−	1.64888i	3.83420	+	2.21368i	−1.98281	−	1.14478i			2.68642i	5.98776			−2.43505	+	1.40588i
353.15	−1.21522	−	0.701610i	0.665795			−0.0154872	−	0.0268246i	−1.61066	+	2.78975i	−0.809089	−	0.467128i	0.374004	+	0.215931i			2.84990i	−2.55672			3.91463	−	2.26011i
353.16	−1.00471	−	0.580068i	0.804932			−0.327042	−	0.566454i	1.36581	−	2.36566i	−0.808721	−	0.466915i	−0.143518	−	0.0828603i			3.07910i	−2.35209			−2.74448	+	1.58453i
353.17	−0.948162	−	0.547422i	2.71191			−0.400659	−	0.693961i	−0.354654	+	0.614279i	−2.57133	−	1.48456i	2.06456	+	1.19197i			3.06700i	4.35444			0.672540	−	0.388291i
353.18	−0.697945	−	0.402959i	1.97028			−0.675248	−	1.16956i	−1.47722	+	2.55862i	−1.37515	−	0.793941i	−1.60723	−	0.927937i			2.70022i	0.881997			2.06204	−	1.19052i
353.19	−0.582930	−	0.336555i	−2.24487			−0.773462	−	1.33968i	0.278495	−	0.482368i	1.30860	+	0.755521i	1.53539	+	0.886457i			2.38747i	2.03943			−0.324687	+	0.187458i
353.20	−0.529811	−	0.305887i	−1.44271			−0.812867	−	1.40793i	−0.00570608	+	0.00988322i	0.764366	+	0.441307i	−1.63348	−	0.943088i			2.21813i	−0.918576			0.00604629	−	0.00349083i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
61.f	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	671.2.o.a	✓	100
61.f	even	6	1	inner	671.2.o.a	✓	100

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
671.2.o.a	✓	100	1.a	even	1	1	trivial
671.2.o.a	✓	100	61.f	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(671, [\chi])\).