Newform orbit 935.2.cf.a

• Label: 935.2.cf.a
• Level: $935$
• Weight: $2$
• Character orbit: 935.cf
• 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.cf (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.

\(\operatorname{Tr}(f)(q) = \) \( 1664 q - 12 q^{3} - 400 q^{4} - 20 q^{5} - 40 q^{6} - 40 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−0.852107	+	2.62252i	0.370592	+	1.54363i	−4.53347	−	3.29376i	1.63200	−	1.52859i	−4.36397	−	0.343452i	−0.121788	+	0.507285i	8.03926	−	5.84086i	0.427576	−	0.217861i	2.61811	+	5.58246i
2.2	−0.842300	+	2.59233i	−0.272345	−	1.13440i	−4.39269	−	3.19148i	0.702562	+	2.12283i	3.17013	+	0.249495i	−0.619480	+	2.58032i	7.56300	−	5.49484i	1.46033	−	0.744078i	−6.09485	+	0.0332144i
2.3	−0.812166	+	2.49959i	0.665214	+	2.77081i	−3.97030	−	2.88459i	−1.47805	+	1.67791i	−7.46616	−	0.587600i	−0.256649	+	1.06902i	6.18228	−	4.49169i	−4.56188	+	2.32439i	−2.99367	−	5.05725i
2.4	−0.791383	+	2.43563i	0.162054	+	0.675004i	−3.68795	−	2.67945i	2.23513	−	0.0648335i	−1.77230	−	0.139483i	−0.308265	+	1.28401i	5.30099	−	3.85140i	2.24365	−	1.14320i	−1.61093	+	5.49524i
2.5	−0.790282	+	2.43224i	−0.634820	−	2.64421i	−3.67321	−	2.66874i	2.14308	+	0.638138i	6.93305	+	0.545643i	0.278699	−	1.16087i	5.25591	−	3.81864i	−3.91585	+	1.99523i	−3.24574	+	4.70817i
2.6	−0.788912	+	2.42802i	−0.453779	−	1.89012i	−3.65487	−	2.65542i	0.252568	−	2.22176i	4.94726	+	0.389357i	0.797293	−	3.32096i	5.20000	−	3.77802i	−0.693637	+	0.353426i	5.19522	+	2.36601i
2.7	−0.787699	+	2.42429i	0.294896	+	1.22833i	−3.63866	−	2.64364i	−2.02140	−	0.956012i	−3.21012	−	0.252642i	0.124153	−	0.517135i	5.15068	−	3.74219i	1.25118	−	0.637510i	3.90990	−	4.14739i
2.8	−0.786437	+	2.42041i	0.284787	+	1.18622i	−3.62184	−	2.63142i	0.529355	+	2.17251i	−3.09511	−	0.243590i	0.986630	−	4.10961i	5.09963	−	3.70510i	1.34700	−	0.686329i	−5.67465	−	0.427285i
2.9	−0.752523	+	2.31603i	−0.0137014	−	0.0570703i	−3.17966	−	2.31016i	−1.83571	−	1.27677i	0.142487	+	0.0112140i	−0.721980	+	3.00726i	3.80290	−	2.76297i	2.66995	−	1.36041i	4.33846	−	3.29076i
2.10	−0.735379	+	2.26327i	−0.623156	−	2.59563i	−2.96355	−	2.15315i	−2.18289	+	0.484748i	6.33285	+	0.498406i	0.0470726	−	0.196071i	3.20198	−	2.32638i	−3.67595	+	1.87299i	0.508141	−	5.29694i
2.11	−0.711073	+	2.18846i	0.721844	+	3.00670i	−2.66569	−	1.93674i	−0.313670	−	2.21396i	−7.09332	−	0.558257i	−0.971850	+	4.04805i	2.41075	−	1.75151i	−5.84616	+	2.97877i	5.06820	+	0.887834i
2.12	−0.701830	+	2.16001i	−0.240777	−	1.00291i	−2.55504	−	1.85635i	0.0282290	−	2.23589i	2.33527	+	0.183790i	0.375830	−	1.56544i	2.12810	−	1.54616i	1.72517	−	0.879018i	4.80973	+	1.63019i
2.13	−0.699357	+	2.15240i	−0.0997798	−	0.415613i	−2.52570	−	1.83502i	−1.66980	+	1.48721i	0.964347	+	0.0758957i	−1.03222	+	4.29949i	2.05419	−	1.49246i	2.51024	−	1.27903i	−2.03328	−	4.63416i
2.14	−0.673741	+	2.07356i	0.446951	+	1.86168i	−2.22770	−	1.61852i	1.95659	−	1.08247i	−4.16145	−	0.327513i	0.876750	−	3.65192i	1.32923	−	0.965743i	−0.593086	+	0.302192i	0.926330	+	4.78642i
2.15	−0.630634	+	1.94089i	−0.301436	−	1.25557i	−1.75133	−	1.27241i	2.23407	−	0.0945257i	2.62702	+	0.206751i	−0.278964	+	1.16197i	0.272024	−	0.197637i	1.18743	−	0.605023i	−1.22542	+	4.39570i
2.16	−0.628295	+	1.93369i	0.564483	+	2.35124i	−1.72639	−	1.25429i	1.83871	+	1.27246i	−4.90125	−	0.385736i	−0.740434	+	3.08413i	0.220302	−	0.160059i	−2.53668	+	1.29250i	−3.61580	+	2.75602i
2.17	−0.625772	+	1.92593i	0.518523	+	2.15980i	−1.69957	−	1.23481i	0.517844	+	2.17528i	−4.48410	−	0.352906i	0.293777	−	1.22367i	0.165117	−	0.119965i	−1.72287	+	0.877844i	−4.51348	−	0.363897i
2.18	−0.620142	+	1.90860i	−0.0749850	−	0.312335i	−1.64015	−	1.19164i	−1.51356	+	1.64594i	0.642624	+	0.0505756i	0.609382	−	2.53826i	0.0443775	−	0.0322421i	2.58109	−	1.31513i	−2.20283	−	3.90950i
2.19	−0.605998	+	1.86507i	0.676203	+	2.81659i	−1.49322	−	1.08489i	−2.21129	−	0.331965i	−5.66292	−	0.445681i	0.781786	−	3.25637i	−0.244760	+	0.177828i	−4.80290	+	2.44720i	1.95918	−	3.92304i
2.20	−0.591504	+	1.82046i	−0.361485	−	1.50569i	−1.34618	−	0.978054i	1.57043	−	1.59177i	2.95488	+	0.232554i	−1.18820	+	4.94921i	−0.520378	+	0.378077i	0.536579	−	0.273401i	1.96884	+	3.80046i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.d	odd	10	1	inner
85.k	odd	8	1	inner
935.cf	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.cf.a	✓	1664
5.c	odd	4	1		935.2.cl.a	yes	1664
11.d	odd	10	1	inner	935.2.cf.a	✓	1664
17.d	even	8	1		935.2.cl.a	yes	1664
55.l	even	20	1		935.2.cl.a	yes	1664
85.k	odd	8	1	inner	935.2.cf.a	✓	1664
187.q	odd	40	1		935.2.cl.a	yes	1664
935.cf	even	40	1	inner	935.2.cf.a	✓	1664

    

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

Hecke kernels

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