Newform orbit 912.2.cq.a

• Label: 912.2.cq.a
• Level: $912$
• Weight: $2$
• Character orbit: 912.cq
• Analytic conductor: $7.282$
• Analytic rank: $0$
• Dimension: $960$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.cq (of order \(36\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.28235666434\)
Analytic rank:	\(0\)
Dimension:	\(960\)
Relative dimension:	\(80\) over \(\Q(\zeta_{36})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 960 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
61.1	−1.41417	−	0.0105175i	0.573576	−	0.819152i	1.99978	+	0.0297471i	−0.185054	+	2.11517i	−0.819753	+	1.15239i	3.92691	+	2.26720i	−2.82772	−	0.0631002i	−0.342020	−	0.939693i	0.283944	−	2.98928i
61.2	−1.40759	−	0.136745i	−0.573576	+	0.819152i	1.96260	+	0.384960i	0.316025	−	3.61219i	0.919373	−	1.07459i	3.11578	+	1.79890i	−2.70989	−	0.810240i	−0.342020	−	0.939693i	−0.938780	+	5.04125i
61.3	−1.40641	+	0.148362i	−0.573576	+	0.819152i	1.95598	−	0.417315i	−0.127730	+	1.45996i	0.685153	−	1.23716i	1.85833	+	1.07291i	−2.68899	+	0.877107i	−0.342020	−	0.939693i	−0.0369615	−	2.07226i
61.4	−1.39841	−	0.210799i	−0.573576	+	0.819152i	1.91113	+	0.589569i	−0.0228711	+	0.261418i	0.974774	−	1.02460i	−4.36365	−	2.51935i	−2.54827	−	1.22733i	−0.342020	−	0.939693i	0.0870900	−	0.360750i
61.5	−1.35214	+	0.414402i	0.573576	−	0.819152i	1.65654	−	1.12065i	0.00787462	−	0.0900073i	−0.436095	+	1.34530i	−0.530826	−	0.306472i	−1.77547	+	2.20175i	−0.342020	−	0.939693i	0.0266516	+	0.124965i
61.6	−1.34797	+	0.427763i	−0.573576	+	0.819152i	1.63404	−	1.15322i	−0.279513	+	3.19484i	0.422760	−	1.34955i	1.76943	+	1.02158i	−1.70933	+	2.25349i	−0.342020	−	0.939693i	−0.989862	−	4.42611i
61.7	−1.34655	+	0.432205i	0.573576	−	0.819152i	1.62640	−	1.16397i	0.262520	−	3.00062i	−0.418308	+	1.35093i	−1.22756	−	0.708732i	−1.68695	+	2.27029i	−0.342020	−	0.939693i	0.943386	+	4.15395i
61.8	−1.34298	−	0.443182i	0.573576	−	0.819152i	1.60718	+	1.19037i	−0.144329	+	1.64968i	−1.13333	+	0.845904i	0.421686	+	0.243460i	−1.63086	−	2.31091i	−0.342020	−	0.939693i	0.924942	−	2.15153i
61.9	−1.33768	−	0.458937i	0.573576	−	0.819152i	1.57875	+	1.22782i	0.296315	−	3.38690i	−1.14320	+	0.832525i	−2.67441	−	1.54407i	−1.54837	−	2.36697i	−0.342020	−	0.939693i	−1.95075	+	4.39458i
61.10	−1.30230	−	0.551386i	0.573576	−	0.819152i	1.39195	+	1.43614i	0.212428	−	2.42806i	−1.19864	+	0.750516i	−0.113967	−	0.0657991i	−1.02086	−	2.63777i	−0.342020	−	0.939693i	−1.61544	+	3.04492i
61.11	−1.28748	+	0.585141i	−0.573576	+	0.819152i	1.31522	−	1.50672i	0.310431	−	3.54824i	0.259150	−	1.39027i	−2.94135	−	1.69819i	−0.811680	+	2.70946i	−0.342020	−	0.939693i	1.67655	+	4.74994i
61.12	−1.28745	−	0.585209i	−0.573576	+	0.819152i	1.31506	+	1.50686i	−0.220228	+	2.51721i	1.21783	−	0.718956i	−1.56519	−	0.903663i	−0.811252	−	2.70959i	−0.342020	−	0.939693i	1.75663	−	3.11191i
61.13	−1.26500	+	0.632271i	0.573576	−	0.819152i	1.20047	−	1.59965i	−0.0862589	+	0.985944i	−0.207650	+	1.39889i	1.07572	+	0.621065i	−0.507185	+	2.78258i	−0.342020	−	0.939693i	−0.514266	−	1.30176i
61.14	−1.19245	−	0.760297i	0.573576	−	0.819152i	0.843897	+	1.81324i	−0.265875	+	3.03896i	−1.30676	+	0.540713i	−2.84983	−	1.64535i	0.372292	−	2.80382i	−0.342020	−	0.939693i	2.62756	−	3.42168i
61.15	−1.16252	+	0.805329i	0.573576	−	0.819152i	0.702889	−	1.87242i	−0.324594	+	3.71013i	−0.00710482	+	1.41420i	−0.901527	−	0.520497i	0.690793	+	2.74277i	−0.342020	−	0.939693i	−2.61053	−	4.57449i
61.16	−1.15998	+	0.808972i	−0.573576	+	0.819152i	0.691128	−	1.87679i	−0.146489	+	1.67438i	0.00266857	−	1.41421i	−2.85916	−	1.65074i	0.716573	+	2.73615i	−0.342020	−	0.939693i	−1.18460	−	2.06076i
61.17	−1.14867	−	0.824961i	−0.573576	+	0.819152i	0.638877	+	1.89521i	0.0740898	−	0.846851i	1.33462	−	0.467755i	2.19181	+	1.26544i	0.829621	−	2.70402i	−0.342020	−	0.939693i	−0.783724	+	0.911629i
61.18	−1.12099	+	0.862198i	−0.573576	+	0.819152i	0.513229	−	1.93303i	−0.0169830	+	0.194117i	−0.0632988	−	1.41280i	1.75541	+	1.01349i	1.09133	+	2.60941i	−0.342020	−	0.939693i	−0.148330	−	0.232246i
61.19	−1.09731	−	0.892137i	−0.573576	+	0.819152i	0.408182	+	1.95790i	0.252527	−	2.88640i	1.36019	−	0.387155i	−1.82753	−	1.05513i	1.29882	−	2.51258i	−0.342020	−	0.939693i	−2.85216	+	2.94199i
61.20	−1.04968	−	0.947718i	0.573576	−	0.819152i	0.203661	+	1.98960i	0.216931	−	2.47953i	−1.37840	+	0.316260i	3.84449	+	2.21962i	1.67180	−	2.28146i	−0.342020	−	0.939693i	−2.57760	+	2.39713i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
16.e	even	4	1	inner
19.e	even	9	1	inner
304.bi	even	36	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	912.2.cq.a	✓	960
16.e	even	4	1	inner	912.2.cq.a	✓	960
19.e	even	9	1	inner	912.2.cq.a	✓	960
304.bi	even	36	1	inner	912.2.cq.a	✓	960

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
912.2.cq.a	✓	960	1.a	even	1	1	trivial
912.2.cq.a	✓	960	16.e	even	4	1	inner
912.2.cq.a	✓	960	19.e	even	9	1	inner
912.2.cq.a	✓	960	304.bi	even	36	1	inner

Hecke kernels

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