Newform orbit 672.2.ch.a

• Label: 672.2.ch.a
• Level: $672$
• Weight: $2$
• Character orbit: 672.ch
• Analytic conductor: $5.366$
• Analytic rank: $0$
• Dimension: $992$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.ch (of order \(24\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.36594701583\)
Analytic rank:	\(0\)
Dimension:	\(992\)
Relative dimension:	\(124\) over \(\Q(\zeta_{24})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−1.41421	+	0.00202033i	−1.50647	+	0.854722i	1.99999	−	0.00571435i	0.202706	+	1.53970i	2.12874	−	1.21180i	0.529096	+	2.59231i	−2.82840	+	0.0121219i	1.53890	−	2.57522i	−0.289779	−	2.17705i
11.2	−1.41371	+	0.0378977i	−1.72802	−	0.118141i	1.99713	−	0.107152i	0.525322	+	3.99022i	2.44738	+	0.101529i	−2.15734	−	1.53163i	−2.81929	+	0.227168i	2.97209	+	0.408300i	−0.893871	−	5.62109i
11.3	−1.41292	+	0.0604964i	0.856964	−	1.50520i	1.99268	−	0.170953i	0.139662	+	1.06084i	−1.11976	+	2.17856i	−1.22300	+	2.34612i	−2.80515	+	0.362093i	−1.53123	−	2.57980i	−0.261508	−	1.49043i
11.4	−1.40999	+	0.109279i	1.70442	−	0.308130i	1.97612	−	0.308164i	−0.270326	−	2.05333i	−2.36954	+	0.620717i	−2.18436	−	1.49283i	−2.75262	+	0.650455i	2.81011	−	1.05037i	0.605541	+	2.86562i
11.5	−1.40871	+	0.124645i	0.277691	+	1.70965i	1.96893	−	0.351176i	−0.255599	−	1.94146i	−0.604284	−	2.37378i	2.57575	+	0.604593i	−2.72988	+	0.740122i	−2.84578	+	0.949506i	0.602057	+	2.70310i
11.6	−1.40759	−	0.136707i	−1.57871	+	0.712503i	1.96262	+	0.384854i	−0.304006	−	2.30915i	2.31959	−	0.787091i	2.28276	−	1.33754i	−2.70996	−	0.810020i	1.98468	−	2.24968i	0.112239	+	3.29190i
11.7	−1.40248	+	0.181762i	−0.483335	−	1.66325i	1.93393	−	0.509836i	−0.549309	−	4.17241i	0.980185	+	2.24482i	1.13563	+	2.38963i	−2.61963	+	1.06655i	−2.53277	+	1.60781i	1.52878	+	5.75190i
11.8	−1.38980	−	0.261641i	1.00222	+	1.41264i	1.86309	+	0.727258i	0.0693882	+	0.527056i	−1.02328	−	2.22551i	−0.176243	−	2.63987i	−2.39904	−	1.49820i	−0.991114	+	2.83155i	0.0414639	−	0.750657i
11.9	−1.36685	+	0.362941i	−0.0108601	+	1.73202i	1.73655	−	0.992170i	0.167832	+	1.27481i	−0.613775	−	2.37135i	−2.51370	+	0.825424i	−2.01350	+	1.98641i	−2.99976	−	0.0376198i	−0.692080	−	1.68156i
11.10	−1.35950	−	0.389562i	−0.721966	−	1.57441i	1.69648	+	1.05922i	0.456804	+	3.46977i	0.368183	+	2.42166i	2.57029	+	0.627378i	−1.89374	−	2.10089i	−1.95753	+	2.27334i	0.730665	−	4.89511i
11.11	−1.34787	+	0.428079i	−1.11026	−	1.32941i	1.63350	−	1.15399i	−0.0969257	−	0.736224i	2.06557	+	1.31659i	−1.56934	−	2.13007i	−1.70774	+	2.25469i	−0.534654	+	2.95197i	0.445805	+	0.950841i
11.12	−1.34744	+	0.429412i	0.649335	−	1.60573i	1.63121	−	1.15722i	0.323918	+	2.46040i	−0.185422	+	2.44246i	1.39830	−	2.24605i	−1.70104	+	2.25975i	−2.15673	−	2.08531i	−1.49299	−	3.17616i
11.13	−1.33331	+	0.471485i	1.63784	+	0.563452i	1.55540	−	1.25727i	0.441991	+	3.35725i	−2.44940	+	0.0209633i	1.71134	+	2.01775i	−1.48105	+	2.40967i	2.36504	+	1.84569i	−2.17220	−	4.26785i
11.14	−1.33152	−	0.476511i	−1.64402	−	0.545154i	1.54587	+	1.26897i	−0.104982	−	0.797415i	1.92927	+	1.50928i	1.28932	−	2.31034i	−1.45368	−	2.42628i	2.40561	+	1.79249i	−0.240192	+	1.11180i
11.15	−1.32881	−	0.484014i	1.60040	−	0.662368i	1.53146	+	1.28632i	0.0620289	+	0.471156i	−2.44721	+	0.105546i	2.10333	+	1.60499i	−1.41242	−	2.45052i	2.12254	−	2.12010i	0.145622	−	0.656099i
11.16	−1.32769	−	0.487083i	−0.590581	+	1.62826i	1.52550	+	1.29339i	−0.520784	−	3.95575i	1.57720	−	1.87415i	−2.59797	+	0.500553i	−1.39540	−	2.46026i	−2.30243	−	1.92323i	−1.23534	+	5.50565i
11.17	−1.30196	−	0.552168i	0.204575	−	1.71993i	1.39022	+	1.43781i	−0.306137	−	2.32534i	−1.21604	+	2.12632i	−1.51022	−	2.17238i	−1.01611	−	2.63961i	−2.91630	−	0.703709i	−0.885400	+	3.19655i
11.18	−1.30144	−	0.553394i	1.57447	+	0.721834i	1.38751	+	1.44042i	0.510185	+	3.87524i	−1.64963	−	1.81073i	−2.48556	+	0.906631i	−1.00865	−	2.64247i	1.95791	+	2.27301i	1.48056	−	5.32573i
11.19	−1.24175	+	0.676794i	−1.72435	+	0.163175i	1.08390	−	1.68082i	−0.337107	−	2.56058i	2.03078	−	1.36965i	−2.18342	+	1.49422i	−0.208366	+	2.82074i	2.94675	−	0.562741i	2.15159	+	2.95146i
11.20	−1.24127	−	0.677674i	−1.06907	−	1.36275i	1.08152	+	1.68236i	0.0342867	+	0.260434i	0.403515	+	2.41602i	−2.18554	+	1.49111i	−0.202366	−	2.82118i	−0.714158	+	2.91376i	0.133930	−	0.346504i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
7.c	even	3	1	inner
21.h	odd	6	1	inner
32.h	odd	8	1	inner
96.o	even	8	1	inner
224.bf	odd	24	1	inner
672.ch	even	24	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	672.2.ch.a	✓	992
3.b	odd	2	1	inner	672.2.ch.a	✓	992
7.c	even	3	1	inner	672.2.ch.a	✓	992
21.h	odd	6	1	inner	672.2.ch.a	✓	992
32.h	odd	8	1	inner	672.2.ch.a	✓	992
96.o	even	8	1	inner	672.2.ch.a	✓	992
224.bf	odd	24	1	inner	672.2.ch.a	✓	992
672.ch	even	24	1	inner	672.2.ch.a	✓	992

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
672.2.ch.a	✓	992	1.a	even	1	1	trivial
672.2.ch.a	✓	992	3.b	odd	2	1	inner
672.2.ch.a	✓	992	7.c	even	3	1	inner
672.2.ch.a	✓	992	21.h	odd	6	1	inner
672.2.ch.a	✓	992	32.h	odd	8	1	inner
672.2.ch.a	✓	992	96.o	even	8	1	inner
672.2.ch.a	✓	992	224.bf	odd	24	1	inner
672.2.ch.a	✓	992	672.ch	even	24	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(672, [\chi])\).