Newform orbit 276.2.o.a

• Label: 276.2.o.a
• Level: $276$
• Weight: $2$
• Character orbit: 276.o
• Analytic conductor: $2.204$
• Analytic rank: $0$
• Dimension: $440$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.o (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.20387109579\)
Analytic rank:	\(0\)
Dimension:	\(440\)
Relative dimension:	\(44\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
35.1	−1.41343	+	0.0471244i	−1.43832	+	0.965005i	1.99556	−	0.133214i	1.15864	+	3.94597i	1.98749	−	1.43174i	−1.89500	+	1.64203i	−2.81430	+	0.282328i	1.13753	−	2.77597i	−1.82361	−	5.52274i
35.2	−1.41336	−	0.0490491i	1.04993	−	1.37755i	1.99519	+	0.138648i	0.512900	+	1.74678i	−1.55150	+	1.89548i	3.04781	−	2.64094i	−2.81312	−	0.293822i	−0.795302	−	2.89266i	−0.639236	−	2.49399i
35.3	−1.39810	+	0.212891i	1.33549	+	1.10293i	1.90935	−	0.595285i	−0.168792	−	0.574851i	−2.10195	−	1.25769i	−2.73269	+	2.36789i	−2.54273	+	1.23875i	0.567081	+	2.94592i	0.358368	+	0.767764i
35.4	−1.38733	+	0.274446i	−1.69492	−	0.356694i	1.84936	−	0.761494i	−0.803645	−	2.73696i	2.44931	+	0.0296852i	0.489256	−	0.423943i	−2.35668	+	1.56399i	2.74554	+	1.20914i	1.86607	+	3.57651i
35.5	−1.34998	−	0.421356i	−0.574135	+	1.63413i	1.64492	+	1.13765i	−0.494860	−	1.68534i	1.46362	−	1.96413i	1.60533	−	1.39102i	−1.74126	−	2.22890i	−2.34074	−	1.87642i	−0.0420733	+	2.48370i
35.6	−1.31697	−	0.515366i	−0.275571	−	1.70999i	1.46880	+	1.35744i	0.241048	+	0.820935i	−0.518352	+	2.39402i	−2.26976	+	1.96676i	−1.23478	−	2.54467i	−2.84812	+	0.942447i	0.105630	−	1.20537i
35.7	−1.20977	+	0.732426i	−0.914165	−	1.47116i	0.927105	−	1.77214i	0.605787	+	2.06312i	2.18345	+	1.11021i	0.738126	−	0.639590i	0.176372	+	2.82292i	−1.32861	+	2.68976i	−2.24395	−	2.05222i
35.8	−1.16880	+	0.796188i	1.29161	−	1.15401i	0.732168	−	1.86116i	−0.605787	−	2.06312i	−0.590813	+	2.37717i	−0.738126	+	0.639590i	0.626082	+	2.75826i	0.336500	−	2.98107i	2.35068	+	1.92905i
35.9	−1.12871	−	0.852070i	1.60391	−	0.653824i	0.547953	+	1.92347i	0.250263	+	0.852318i	−2.36744	−	0.628665i	−1.73353	+	1.50211i	1.02046	−	2.63793i	2.14503	−	2.09735i	0.443761	−	1.17526i
35.10	−1.09972	−	0.889160i	0.954066	+	1.44560i	0.418787	+	1.95566i	0.982607	+	3.34645i	0.236161	−	2.43808i	0.453842	−	0.393256i	1.27835	−	2.52306i	−1.17952	+	2.75839i	1.89494	−	4.55387i
35.11	−1.00830	−	0.991633i	−1.72667	−	0.136433i	0.0333293	+	1.99972i	−0.252117	−	0.858632i	1.60571	+	1.84979i	−1.92220	+	1.66560i	1.94938	−	2.04937i	2.96277	+	0.471148i	−0.597239	+	1.11576i
35.12	−0.932383	−	1.06333i	−0.322706	−	1.70172i	−0.261325	+	1.98285i	−1.00656	−	3.42802i	−1.50860	+	1.92980i	3.30235	−	2.86150i	2.35207	−	1.57091i	−2.79172	+	1.09831i	−2.70660	+	4.26652i
35.13	−0.825962	+	1.14795i	1.72676	+	0.135270i	−0.635573	−	1.89632i	0.803645	+	2.73696i	−1.58152	+	1.87050i	−0.489256	+	0.423943i	2.70184	+	0.836687i	2.96340	+	0.467159i	−3.80567	−	1.33808i
35.14	−0.774443	+	1.18332i	−1.59213	+	0.682004i	−0.800475	−	1.83282i	0.168792	+	0.574851i	0.425987	−	2.41216i	2.73269	−	2.36789i	2.78873	+	0.472203i	2.06974	−	2.17167i	−0.810951	−	0.245456i
35.15	−0.630025	+	1.26612i	1.10819	+	1.33114i	−1.20614	−	1.59538i	−1.15864	−	3.94597i	−2.38357	+	0.564449i	1.89500	−	1.64203i	2.77984	−	0.521989i	−0.543851	+	2.95029i	5.72606	+	1.01908i
35.16	−0.579910	−	1.28985i	0.322706	+	1.70172i	−1.32741	+	1.49599i	−1.00656	−	3.42802i	2.00782	−	1.40309i	−3.30235	+	2.86150i	2.69937	+	0.844617i	−2.79172	+	1.09831i	−3.83790	+	3.28624i
35.17	−0.542515	+	1.30602i	−0.619297	−	1.61755i	−1.41135	−	1.41707i	−0.512900	−	1.74678i	2.44853	+	0.0687346i	−3.04781	+	2.64094i	2.61639	−	1.07447i	−2.23294	+	2.00349i	2.55957	+	0.277798i
35.18	−0.483159	−	1.32912i	1.72667	+	0.136433i	−1.53312	+	1.28435i	−0.252117	−	0.858632i	−0.652920	−	2.36087i	1.92220	−	1.66560i	2.44779	+	1.41715i	2.96277	+	0.471148i	−1.01941	+	0.749950i
35.19	−0.351967	−	1.36972i	−0.954066	−	1.44560i	−1.75224	+	0.964188i	0.982607	+	3.34645i	−1.64426	+	1.81560i	−0.453842	+	0.393256i	1.93739	+	2.06071i	−1.17952	+	2.75839i	4.23784	−	2.52373i
35.20	−0.306189	−	1.38067i	−1.60391	+	0.653824i	−1.81250	+	0.845492i	0.250263	+	0.852318i	1.39381	+	2.01427i	1.73353	−	1.50211i	1.72231	+	2.24358i	2.14503	−	2.09735i	1.10014	−	0.606501i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
4.b	odd	2	1	inner
12.b	even	2	1	inner
23.c	even	11	1	inner
69.h	odd	22	1	inner
92.g	odd	22	1	inner
276.o	even	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	276.2.o.a	✓	440
3.b	odd	2	1	inner	276.2.o.a	✓	440
4.b	odd	2	1	inner	276.2.o.a	✓	440
12.b	even	2	1	inner	276.2.o.a	✓	440
23.c	even	11	1	inner	276.2.o.a	✓	440
69.h	odd	22	1	inner	276.2.o.a	✓	440
92.g	odd	22	1	inner	276.2.o.a	✓	440
276.o	even	22	1	inner	276.2.o.a	✓	440

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
276.2.o.a	✓	440	1.a	even	1	1	trivial
276.2.o.a	✓	440	3.b	odd	2	1	inner
276.2.o.a	✓	440	4.b	odd	2	1	inner
276.2.o.a	✓	440	12.b	even	2	1	inner
276.2.o.a	✓	440	23.c	even	11	1	inner
276.2.o.a	✓	440	69.h	odd	22	1	inner
276.2.o.a	✓	440	92.g	odd	22	1	inner
276.2.o.a	✓	440	276.o	even	22	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(276, [\chi])\).