Newform orbit 931.2.bz.a

• Label: 931.2.bz.a
• Level: $931$
• Weight: $2$
• Character orbit: 931.bz
• Analytic conductor: $7.434$
• Analytic rank: $0$
• Dimension: $1104$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.bz (of order \(42\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.43407242818\)
Analytic rank:	\(0\)
Dimension:	\(1104\)
Relative dimension:	\(92\) over \(\Q(\zeta_{42})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1104 q - 21 q^{2} - 18 q^{3} + 179 q^{4} - 7 q^{5} - 19 q^{6} - 24 q^{7} + 82 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
12.1	−1.21227	+	2.51731i	−2.73340	−	0.843142i	−3.62026	−	4.53967i	3.82484	−	0.872995i	5.43607	−	5.85869i	0.0575287	−	2.64513i	10.3686	−	2.36656i	4.28186	+	2.91933i	−2.43915	+	10.6866i
12.2	−1.20748	+	2.50736i	0.459589	+	0.141764i	−3.58187	−	4.49152i	−2.11927	+	0.483711i	−0.910400	+	0.981178i	−0.624306	−	2.57104i	10.1605	−	2.31908i	−2.28759	−	1.55965i	1.34615	−	5.89786i
12.3	−1.14091	+	2.36913i	0.578267	+	0.178372i	−3.06412	−	3.84228i	−3.77289	+	0.861139i	−1.08234	+	1.16648i	1.38707	+	2.25301i	7.47155	−	1.70533i	−2.17614	−	1.48367i	2.26440	−	9.92097i
12.4	−1.13288	+	2.35244i	−1.39536	−	0.430411i	−3.00359	−	3.76638i	−0.185205	+	0.0422719i	2.59329	−	2.79490i	2.31998	+	1.27189i	7.17179	−	1.63692i	−0.716943	−	0.488803i	0.110372	−	0.483573i
12.5	−1.12584	+	2.33782i	3.08841	+	0.952650i	−2.95093	−	3.70035i	−1.21550	+	0.277431i	−5.70418	+	6.14764i	−2.44457	+	1.01196i	6.91357	−	1.57798i	6.15204	+	4.19439i	0.719874	−	3.15397i
12.6	−1.12307	+	2.33208i	1.42747	+	0.440317i	−2.93034	−	3.67453i	2.01304	−	0.459462i	−2.63001	+	2.83448i	−2.54036	+	0.739303i	6.81325	−	1.55508i	−0.634915	−	0.432878i	−1.18928	+	5.21058i
12.7	−1.11585	+	2.31709i	1.44903	+	0.446966i	−2.87679	−	3.60738i	3.82993	−	0.874156i	−2.65256	+	2.85878i	1.67651	+	2.04679i	6.55410	−	1.49593i	−0.578815	−	0.394629i	−2.24813	+	9.84971i
12.8	−1.09852	+	2.28110i	2.71430	+	0.837250i	−2.74971	−	3.44802i	−0.0890799	+	0.0203319i	−4.89157	+	5.27186i	2.45543	−	0.985314i	5.94920	−	1.35787i	4.18770	+	2.85513i	0.0514770	−	0.225535i
12.9	−1.09400	+	2.27172i	−2.73042	−	0.842223i	−2.71689	−	3.40687i	−2.66158	+	0.607489i	4.90038	−	5.28135i	−1.78115	+	1.95640i	5.79532	−	1.32274i	4.26714	+	2.90929i	1.53173	−	6.71097i
12.10	−1.02747	+	2.13356i	−0.153966	−	0.0474924i	−2.24942	−	2.82068i	1.53445	−	0.350228i	0.259524	−	0.279700i	−2.59781	−	0.501404i	3.71190	−	0.847216i	−2.45727	−	1.67534i	−0.829368	+	3.63370i
12.11	−1.02025	+	2.11856i	0.309287	+	0.0954024i	−2.20043	−	2.75925i	0.780884	−	0.178232i	−0.517665	+	0.557910i	1.44195	−	2.21828i	3.50567	−	0.800147i	−2.39216	−	1.63095i	−0.419099	+	1.83619i
12.12	−0.944663	+	1.96161i	−1.76295	−	0.543797i	−1.70856	−	2.14246i	−2.08206	+	0.475217i	2.73211	−	2.94452i	0.141353	−	2.64197i	1.57141	−	0.358664i	0.333554	+	0.227413i	1.03465	−	4.53311i
12.13	−0.942574	+	1.95728i	−2.95746	−	0.912255i	−1.69550	−	2.12609i	−1.40899	+	0.321594i	4.57316	−	4.92869i	2.21731	−	1.44344i	1.52359	−	0.347749i	5.43563	+	3.70595i	0.698634	−	3.06092i
12.14	−0.931367	+	1.93400i	−1.77767	−	0.548339i	−1.62594	−	2.03887i	3.00140	−	0.685050i	2.71615	−	2.92732i	−0.525811	+	2.59298i	1.27200	−	0.290327i	0.380726	+	0.259575i	−1.47051	+	6.44275i
12.15	−0.860751	+	1.78737i	0.476247	+	0.146903i	−1.20681	−	1.51330i	−1.55858	+	0.355736i	−0.672500	+	0.724783i	−1.03401	+	2.43533i	−0.124594	+	0.0284379i	−2.27349	−	1.55004i	0.705719	−	3.09196i
12.16	−0.856405	+	1.77834i	−2.01863	−	0.622666i	−1.18210	−	1.48230i	1.27262	−	0.290468i	2.83608	−	3.05657i	2.07698	+	1.63895i	−0.200251	+	0.0457060i	1.20845	+	0.823909i	−0.573330	+	2.51192i
12.17	−0.851963	+	1.76912i	1.96035	+	0.604689i	−1.15696	−	1.45078i	−3.15850	+	0.720908i	−2.73991	+	2.95293i	−1.02663	−	2.43845i	−0.276391	+	0.0630844i	0.998622	+	0.680849i	1.41556	−	6.20195i
12.18	−0.842322	+	1.74910i	1.06870	+	0.329651i	−1.10286	−	1.38294i	−0.184052	+	0.0420087i	−1.47678	+	1.59159i	−0.254820	+	2.63345i	−0.437487	+	0.0998536i	−1.44526	−	0.985363i	0.0815537	−	0.357310i
12.19	−0.813408	+	1.68906i	2.87830	+	0.887837i	−0.944309	−	1.18413i	2.52926	−	0.577288i	−3.84084	+	4.13944i	0.0617989	−	2.64503i	−0.887254	+	0.202510i	5.01762	+	3.42096i	−1.08225	+	4.74165i
12.20	−0.800146	+	1.66152i	−1.50394	−	0.463905i	−0.873437	−	1.09526i	3.08334	−	0.703752i	1.97416	−	2.12764i	−2.40696	−	1.09844i	−1.07716	+	0.245854i	−0.432075	−	0.294584i	−1.29782	+	5.68613i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
931.bz	even	42	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	931.2.bz.a	yes	1104
19.d	odd	6	1		931.2.bp.a	✓	1104
49.h	odd	42	1		931.2.bp.a	✓	1104
931.bz	even	42	1	inner	931.2.bz.a	yes	1104

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
931.2.bp.a	✓	1104	19.d	odd	6	1
931.2.bp.a	✓	1104	49.h	odd	42	1
931.2.bz.a	yes	1104	1.a	even	1	1	trivial
931.2.bz.a	yes	1104	931.bz	even	42	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(931, [\chi])\).