Newform orbit 912.2.y.a

• Label: 912.2.y.a
• Level: $912$
• Weight: $2$
• Character orbit: 912.y
• Analytic conductor: $7.282$
• Analytic rank: $0$
• Dimension: $160$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.y (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.28235666434\)
Analytic rank:	\(0\)
Dimension:	\(160\)
Relative dimension:	\(80\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 160 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
379.1	−1.41407	−	0.0204432i	0.707107	−	0.707107i	1.99916	+	0.0578161i	−2.58937	−	2.58937i	−1.01435	+	0.985440i	−0.972310			−2.82577	−	0.122625i		−	1.00000i	3.60861	+	3.71448i
379.2	−1.40580	+	0.153999i	−0.707107	+	0.707107i	1.95257	−	0.432984i	0.558086	+	0.558086i	0.885160	−	1.10295i	−3.00047			−2.67825	+	0.909383i		−	1.00000i	−0.870503	−	0.698614i
379.3	−1.40510	+	0.160293i	0.707107	−	0.707107i	1.94861	−	0.450456i	−0.0122491	−	0.0122491i	−0.880211	+	1.10690i	−0.235561			−2.66579	+	0.945286i		−	1.00000i	0.0191746	+	0.0152477i
379.4	−1.40265	−	0.180457i	0.707107	−	0.707107i	1.93487	+	0.506238i	2.95999	+	2.95999i	−1.11943	+	0.864223i	−5.10964			−2.62260	−	1.05924i		−	1.00000i	−3.61768	−	4.68598i
379.5	−1.40183	+	0.186764i	0.707107	−	0.707107i	1.93024	−	0.523622i	1.64329	+	1.64329i	−0.859179	+	1.12330i	2.82994			−2.60807	+	1.09453i		−	1.00000i	−2.61051	−	1.99670i
379.6	−1.40040	−	0.197198i	−0.707107	+	0.707107i	1.92223	+	0.552312i	−1.37312	−	1.37312i	1.12967	−	0.850790i	1.14430			−2.58296	−	1.15252i		−	1.00000i	1.65213	+	2.19369i
379.7	−1.38606	−	0.280768i	−0.707107	+	0.707107i	1.84234	+	0.778325i	0.376028	+	0.376028i	1.17863	−	0.781561i	3.26839			−2.33507	−	1.59608i		−	1.00000i	−0.415622	−	0.626775i
379.8	−1.37072	−	0.348042i	0.707107	−	0.707107i	1.75773	+	0.954136i	−1.77739	−	1.77739i	−1.21535	+	0.723140i	−1.54998			−2.07728	−	1.91962i		−	1.00000i	1.81770	+	3.05492i
379.9	−1.35115	+	0.417616i	−0.707107	+	0.707107i	1.65119	−	1.12852i	−1.93786	−	1.93786i	0.660105	−	1.25070i	−0.339330			−1.75971	+	2.21436i		−	1.00000i	3.42761	+	1.80905i
379.10	−1.34341	+	0.441856i	−0.707107	+	0.707107i	1.60953	−	1.18719i	2.32728	+	2.32728i	0.637499	−	1.26238i	1.95660			−1.63770	+	2.30607i		−	1.00000i	−4.15483	−	2.09818i
379.11	−1.29806	−	0.561289i	−0.707107	+	0.707107i	1.36991	+	1.45717i	2.05302	+	2.05302i	1.31476	−	0.520974i	−1.40415			−0.960326	−	2.66041i		−	1.00000i	−1.51260	−	3.81728i
379.12	−1.24813	+	0.664964i	0.707107	−	0.707107i	1.11565	−	1.65992i	−0.304035	−	0.304035i	−0.412359	+	1.35276i	0.146161			−0.288680	+	2.81366i		−	1.00000i	0.581647	+	0.177302i
379.13	−1.18963	+	0.764709i	−0.707107	+	0.707107i	0.830439	−	1.81944i	−2.34584	−	2.34584i	0.300464	−	1.38193i	−4.23687			0.403430	+	2.79951i		−	1.00000i	4.58457	+	0.996797i
379.14	−1.17259	−	0.790587i	0.707107	−	0.707107i	0.749945	+	1.85407i	1.55667	+	1.55667i	−1.38818	+	0.270119i	1.79695			0.586426	−	2.76697i		−	1.00000i	−0.594657	−	3.05603i
379.15	−1.15251	+	0.819586i	−0.707107	+	0.707107i	0.656557	−	1.88916i	1.73084	+	1.73084i	0.235413	−	1.39448i	−1.06139			0.791642	+	2.71538i		−	1.00000i	−3.41338	−	0.576236i
379.16	−1.12264	+	0.860051i	0.707107	−	0.707107i	0.520625	−	1.93105i	−1.32970	−	1.32970i	−0.185676	+	1.40197i	4.72425			1.07633	+	2.61563i		−	1.00000i	2.63639	+	0.349161i
379.17	−1.10524	−	0.882292i	−0.707107	+	0.707107i	0.443121	+	1.95029i	0.119923	+	0.119923i	1.40540	−	0.157650i	4.92984			1.23097	−	2.54651i		−	1.00000i	−0.0267368	−	0.238351i
379.18	−1.07488	−	0.919035i	−0.707107	+	0.707107i	0.310751	+	1.97571i	−2.08486	−	2.08486i	1.40991	−	0.110202i	−3.58441			1.48173	−	2.40925i		−	1.00000i	0.324924	+	4.15704i
379.19	−1.05437	−	0.942502i	0.707107	−	0.707107i	0.223379	+	1.98749i	−1.28603	−	1.28603i	−1.41200	+	0.0791001i	0.715149			1.63769	−	2.30607i		−	1.00000i	0.143861	+	2.56803i
379.20	−1.04440	−	0.953530i	−0.707107	+	0.707107i	0.181562	+	1.99174i	1.29379	+	1.29379i	1.41275	−	0.0642582i	−1.84515			1.70956	−	2.25331i		−	1.00000i	−0.117573	−	2.58490i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
16.f	odd	4	1	inner
19.b	odd	2	1	inner
304.m	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	912.2.y.a	✓	160
16.f	odd	4	1	inner	912.2.y.a	✓	160
19.b	odd	2	1	inner	912.2.y.a	✓	160
304.m	even	4	1	inner	912.2.y.a	✓	160

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
912.2.y.a	✓	160	1.a	even	1	1	trivial
912.2.y.a	✓	160	16.f	odd	4	1	inner
912.2.y.a	✓	160	19.b	odd	2	1	inner
912.2.y.a	✓	160	304.m	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(912, [\chi])\).