Newform orbit 234.2.y.a

• Label: 234.2.y.a
• Level: $234$
• Weight: $2$
• Character orbit: 234.y
• Analytic conductor: $1.868$
• Analytic rank: $0$
• Dimension: $56$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.y (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.86849940730\)
Analytic rank:	\(0\)
Dimension:	\(56\)
Relative dimension:	\(14\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 56 q + 4 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−0.707107	+	0.707107i	−1.69503	−	0.356189i		−	1.00000i	−3.71422	−	0.995221i	1.45043	−	0.946704i	2.11355	+	0.566325i	0.707107	+	0.707107i	2.74626	+	1.20750i	3.33007	−	1.92262i
11.2	−0.707107	+	0.707107i	−1.57210	+	0.726972i		−	1.00000i	0.653109	+	0.175000i	0.597599	−	1.62569i	−3.90017	−	1.04505i	0.707107	+	0.707107i	1.94302	−	2.28575i	−0.585562	+	0.338074i
11.3	−0.707107	+	0.707107i	−1.04058	+	1.38462i		−	1.00000i	1.51706	+	0.406496i	−0.243274	−	1.71488i	4.52587	+	1.21270i	0.707107	+	0.707107i	−0.834373	−	2.88164i	−1.36016	+	0.785290i
11.4	−0.707107	+	0.707107i	0.0694742	−	1.73066i		−	1.00000i	0.339151	+	0.0908752i	1.17463	+	1.27288i	2.97685	+	0.797644i	0.707107	+	0.707107i	−2.99035	−	0.240472i	−0.304074	+	0.175557i
11.5	−0.707107	+	0.707107i	1.09699	+	1.34038i		−	1.00000i	0.994452	+	0.266463i	−1.72348	−	0.172100i	0.339163	+	0.0908784i	0.707107	+	0.707107i	−0.593221	+	2.94076i	−0.891601	+	0.514766i
11.6	−0.707107	+	0.707107i	1.46728	−	0.920381i		−	1.00000i	−3.62177	−	0.970449i	−0.386713	+	1.68833i	−3.13748	−	0.840685i	0.707107	+	0.707107i	1.30580	−	2.70091i	3.24719	−	1.87476i
11.7	−0.707107	+	0.707107i	1.67398	−	0.444746i		−	1.00000i	3.83221	+	1.02684i	−0.869198	+	1.49816i	−1.55176	−	0.415793i	0.707107	+	0.707107i	2.60440	−	1.48899i	−3.43586	+	1.98370i
11.8	0.707107	−	0.707107i	−1.36513	+	1.06603i		−	1.00000i	−3.36565	−	0.901822i	−0.211491	+	1.71909i	0.0541850	+	0.0145188i	−0.707107	−	0.707107i	0.727143	−	2.91054i	−3.01756	+	1.74219i
11.9	0.707107	−	0.707107i	−1.25339	−	1.19541i		−	1.00000i	−0.670386	−	0.179629i	−1.73157	+	0.0409976i	−4.43374	−	1.18802i	−0.707107	−	0.707107i	0.141980	+	2.99664i	−0.601052	+	0.347017i
11.10	0.707107	−	0.707107i	−0.870336	+	1.49750i		−	1.00000i	1.35053	+	0.361873i	0.443474	+	1.67432i	0.977097	+	0.261812i	−0.707107	−	0.707107i	−1.48503	−	2.60666i	1.21085	−	0.699086i
11.11	0.707107	−	0.707107i	−0.539995	−	1.64572i		−	1.00000i	3.04921	+	0.817032i	−1.54554	−	0.781868i	2.84235	+	0.761606i	−0.707107	−	0.707107i	−2.41681	+	1.77736i	2.73384	−	1.57838i
11.12	0.707107	−	0.707107i	1.04323	+	1.38263i		−	1.00000i	1.62665	+	0.435860i	1.71534	+	0.239994i	0.290365	+	0.0778030i	−0.707107	−	0.707107i	−0.823344	+	2.88481i	1.45842	−	0.842018i
11.13	0.707107	−	0.707107i	1.25580	−	1.19288i		−	1.00000i	0.650628	+	0.174335i	0.0444876	−	1.73148i	−1.73068	−	0.463733i	−0.707107	−	0.707107i	0.154059	−	2.99604i	0.583337	−	0.336790i
11.14	0.707107	−	0.707107i	1.72982	+	0.0878497i		−	1.00000i	−2.64098	−	0.707650i	1.28529	−	1.16105i	3.36644	+	0.902034i	−0.707107	−	0.707107i	2.98456	+	0.303929i	−2.36784	+	1.36707i
59.1	−0.707107	+	0.707107i	−1.36368	−	1.06788i		−	1.00000i	0.763001	+	2.84756i	1.71938	−	0.209163i	−0.504962	−	1.88454i	0.707107	+	0.707107i	0.719258	+	2.91250i	−2.55305	−	1.47400i
59.2	−0.707107	+	0.707107i	−0.891650	+	1.48491i		−	1.00000i	−0.491075	−	1.83272i	−0.419498	−	1.68048i	−0.530631	−	1.98034i	0.707107	+	0.707107i	−1.40992	−	2.64804i	1.64317	+	0.948684i
59.3	−0.707107	+	0.707107i	−0.769968	+	1.55150i		−	1.00000i	0.891175	+	3.32591i	−0.552626	−	1.64153i	−0.00737496	−	0.0275237i	0.707107	+	0.707107i	−1.81430	−	2.38921i	−2.98193	−	1.72162i
59.4	−0.707107	+	0.707107i	−0.602491	−	1.62389i		−	1.00000i	−0.594929	−	2.22031i	1.57429	+	0.722235i	0.404840	+	1.51089i	0.707107	+	0.707107i	−2.27401	+	1.95675i	1.99067	+	1.14931i
59.5	−0.707107	+	0.707107i	0.851088	−	1.50853i		−	1.00000i	0.517281	+	1.93052i	0.464878	+	1.66850i	0.686666	+	2.56267i	0.707107	+	0.707107i	−1.55130	−	2.56778i	−1.73086	−	0.999310i
59.6	−0.707107	+	0.707107i	1.05720	+	1.37198i		−	1.00000i	−0.772339	−	2.88241i	−1.71769	−	0.222585i	0.751103	+	2.80315i	0.707107	+	0.707107i	−0.764662	+	2.90091i	2.58430	+	1.49204i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
117.x	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	234.2.y.a	✓	56
3.b	odd	2	1		702.2.bb.a		56
9.c	even	3	1		702.2.bc.a		56
9.d	odd	6	1		234.2.z.a	yes	56
13.f	odd	12	1		234.2.z.a	yes	56
39.k	even	12	1		702.2.bc.a		56
117.w	odd	12	1		702.2.bb.a		56
117.x	even	12	1	inner	234.2.y.a	✓	56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
234.2.y.a	✓	56	1.a	even	1	1	trivial
234.2.y.a	✓	56	117.x	even	12	1	inner
234.2.z.a	yes	56	9.d	odd	6	1
234.2.z.a	yes	56	13.f	odd	12	1
702.2.bb.a		56	3.b	odd	2	1
702.2.bb.a		56	117.w	odd	12	1
702.2.bc.a		56	9.c	even	3	1
702.2.bc.a		56	39.k	even	12	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(234, [\chi])\).