Newform orbit 935.2.cl.a

• Label: 935.2.cl.a
• Level: $935$
• Weight: $2$
• Character orbit: 935.cl
• Analytic conductor: $7.466$
• Analytic rank: $0$
• Dimension: $1664$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.cl (of order \(40\), degree \(16\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.46601258899\)
Analytic rank:	\(0\)
Dimension:	\(1664\)
Relative dimension:	\(104\) over \(\Q(\zeta_{40})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1664 q - 40 q^{2} - 12 q^{3} + 400 q^{4} - 20 q^{5} - 40 q^{6} - 40 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
83.1	−2.63917	+	0.857519i	−2.71158	+	1.66166i	4.61185	−	3.35071i	−0.251444	+	2.22189i	5.73142	−	6.71063i	0.614747	+	0.376717i	−6.03598	+	8.30781i	3.22959	−	6.33842i	−1.24171	−	6.07955i
83.2	−2.56516	+	0.833471i	2.09633	−	1.28463i	4.26734	−	3.10040i	1.80378	−	1.32151i	−4.30671	+	5.04251i	3.21475	+	1.97000i	−5.19160	+	7.14562i	1.38234	−	2.71299i	−3.52554	+	4.89328i
83.3	−2.56422	+	0.833166i	2.51054	−	1.53846i	4.26304	−	3.09728i	−1.92905	+	1.13083i	−5.15579	+	6.03665i	−1.03342	−	0.633278i	−5.18127	+	7.13141i	2.57397	−	5.05171i	4.00434	−	4.50691i
83.4	−2.55806	+	0.831164i	0.728607	−	0.446491i	4.23480	−	3.07676i	−2.00565	−	0.988623i	−1.49271	+	1.74774i	0.960665	+	0.588696i	−5.11364	+	7.03832i	−1.03046	+	2.02239i	5.95227	+	0.861934i
83.5	−2.51938	+	0.818597i	−0.237183	+	0.145346i	4.05915	−	2.94915i	0.638858	+	2.14286i	0.478575	−	0.560340i	0.188248	+	0.115359i	−4.69827	+	6.46662i	−1.32684	+	2.60407i	−3.36367	−	4.87572i
83.6	−2.48290	+	0.806742i	−2.04465	+	1.25296i	3.89591	−	2.83055i	−0.383539	−	2.20293i	4.06583	−	4.76048i	2.33904	+	1.43337i	−4.32060	+	5.94680i	1.24870	−	2.45071i	2.72948	+	5.16023i
83.7	−2.43698	+	0.791822i	1.04080	−	0.637806i	3.69384	−	2.68373i	1.76380	+	1.37442i	−2.03139	+	2.37845i	−2.91881	−	1.78865i	−3.86449	+	5.31902i	−0.685494	+	1.34536i	−5.38663	−	1.95281i
83.8	−2.43568	+	0.791402i	−1.47213	+	0.902121i	3.68820	−	2.67964i	−1.97703	−	1.04468i	2.87170	−	3.36232i	−3.88373	−	2.37995i	−3.85196	+	5.30177i	−0.00863518	+	0.0169475i	5.64218	+	0.979892i
83.9	−2.34369	+	0.761510i	1.95595	−	1.19861i	3.29493	−	2.39391i	0.845743	−	2.06996i	−3.67139	+	4.29864i	−4.26948	−	2.61634i	−3.00235	+	4.13237i	1.02712	−	2.01583i	−0.405863	+	5.49537i
83.10	−2.32458	+	0.755302i	−1.81238	+	1.11063i	3.21516	−	2.33595i	2.13611	−	0.661072i	3.37416	−	3.95064i	0.105121	+	0.0644184i	−2.83621	+	3.90371i	0.689257	−	1.35274i	−4.46626	+	3.15013i
83.11	−2.28484	+	0.742390i	0.494083	−	0.302774i	3.05132	−	2.21692i	−0.412335	−	2.19772i	−0.904124	+	1.05859i	2.69783	+	1.65323i	−2.50175	+	3.44337i	−1.20953	+	2.37383i	2.57369	+	4.71533i
83.12	−2.20921	+	0.717815i	−0.899813	+	0.551406i	2.74731	−	1.99604i	−1.96307	+	1.07068i	1.59207	−	1.86407i	−2.52864	−	1.54955i	−1.90586	+	2.62319i	−0.856356	+	1.68069i	3.56827	−	3.77448i
83.13	−2.19732	+	0.713953i	2.08118	−	1.27535i	2.70046	−	1.96200i	0.0781711	+	2.23470i	−3.66248	+	4.28822i	3.65767	+	2.24142i	−1.81697	+	2.50085i	1.34282	−	2.63544i	−1.76724	−	4.85455i
83.14	−2.06301	+	0.670312i	−0.465616	+	0.285330i	2.18865	−	1.59015i	−1.89757	+	1.18289i	0.769310	−	0.900746i	2.49500	+	1.52894i	−0.899287	+	1.23776i	−1.22659	+	2.40731i	3.12180	−	3.71227i
83.15	−2.05257	+	0.666920i	−2.44637	+	1.49914i	2.15022	−	1.56223i	2.23179	−	0.138184i	4.02154	−	4.70861i	−2.86410	−	1.75512i	−0.834487	+	1.14857i	2.37534	−	4.66186i	−4.48875	+	1.77206i
83.16	−2.04202	+	0.663494i	−0.822733	+	0.504172i	2.11160	−	1.53417i	1.90404	+	1.17244i	1.34553	−	1.57541i	3.91604	+	2.39975i	−0.769954	+	1.05975i	−0.939270	+	1.84342i	−4.66601	−	1.13084i
83.17	−1.95809	+	0.636222i	1.45258	−	0.890143i	1.81130	−	1.31599i	−2.22229	−	0.247862i	−2.27795	+	2.66714i	0.497521	+	0.304881i	−0.289099	+	0.397910i	−0.0443342	+	0.0870108i	4.50913	−	0.928531i
83.18	−1.93025	+	0.627177i	−0.222086	+	0.136094i	1.71449	−	1.24565i	1.35043	−	1.78223i	0.343327	−	0.401984i	−0.876618	−	0.537192i	−0.142239	+	0.195775i	−1.33117	+	2.61257i	−1.48889	+	4.28711i
83.19	−1.92358	+	0.625009i	1.89922	−	1.16384i	1.69149	−	1.22894i	2.22482	+	0.223991i	−2.92589	+	3.42578i	0.0457041	+	0.0280075i	−0.107941	+	0.148568i	0.890535	−	1.74777i	−4.41962	+	0.959668i
83.20	−1.85977	+	0.604276i	0.863739	−	0.529300i	1.47556	−	1.07206i	−0.824058	−	2.07868i	−1.28651	+	1.50631i	−1.03497	−	0.634229i	0.202416	−	0.278602i	−0.896085	+	1.75867i	2.78866	+	3.36792i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.d	odd	10	1	inner
85.n	odd	8	1	inner
935.cl	even	40	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	935.2.cl.a	yes	1664
5.c	odd	4	1		935.2.cf.a	✓	1664
11.d	odd	10	1	inner	935.2.cl.a	yes	1664
17.d	even	8	1		935.2.cf.a	✓	1664
55.l	even	20	1		935.2.cf.a	✓	1664
85.n	odd	8	1	inner	935.2.cl.a	yes	1664
187.q	odd	40	1		935.2.cf.a	✓	1664
935.cl	even	40	1	inner	935.2.cl.a	yes	1664

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
935.2.cf.a	✓	1664	5.c	odd	4	1
935.2.cf.a	✓	1664	17.d	even	8	1
935.2.cf.a	✓	1664	55.l	even	20	1
935.2.cf.a	✓	1664	187.q	odd	40	1
935.2.cl.a	yes	1664	1.a	even	1	1	trivial
935.2.cl.a	yes	1664	11.d	odd	10	1	inner
935.2.cl.a	yes	1664	85.n	odd	8	1	inner
935.2.cl.a	yes	1664	935.cl	even	40	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(935, [\chi])\).