Newform orbit 935.2.cp.a

• Label: 935.2.cp.a
• Level: $935$
• Weight: $2$
• Character orbit: 935.cp
• Analytic conductor: $7.466$
• Analytic rank: $0$
• Dimension: $3328$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.cp (of order \(80\), degree \(32\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.46601258899\)
Analytic rank:	\(0\)
Dimension:	\(3328\)
Relative dimension:	\(104\) over \(\Q(\zeta_{80})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{80}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 3328 q - 48 q^{4} - 24 q^{5} - 80 q^{6} - 48 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
24.1	−2.11734	−	1.80838i	3.11907	−	0.122549i	0.900023	+	5.68252i	−0.501151	−	2.17919i	−6.82575	−	5.38098i	2.06143	−	1.90557i	5.46072	−	8.91108i	6.72284	−	0.529099i	−2.87968	+	5.52034i
24.2	−2.07883	−	1.77549i	0.195125	−	0.00766648i	0.856304	+	5.40649i	−0.691533	+	2.12645i	−0.419243	−	0.330505i	0.325958	−	0.301313i	4.96219	−	8.09756i	−2.95274	+	0.232385i	5.21306	−	3.19271i
24.3	−2.02566	−	1.73007i	−0.399978	+	0.0157152i	0.797258	+	5.03369i	1.44264	−	1.70845i	0.837406	+	0.660158i	−1.96978	+	1.82085i	4.30990	−	7.03312i	−2.83102	+	0.222806i	−5.87803	+	0.964849i
24.4	−2.00567	−	1.71300i	−2.40100	+	0.0943355i	0.775457	+	4.89604i	2.14543	−	0.630180i	4.97720	+	3.92371i	0.799123	−	0.738702i	4.07530	−	6.65029i	2.76515	−	0.217622i	−5.38252	−	2.41119i
24.5	−1.96497	−	1.67824i	0.678329	−	0.0266516i	0.731734	+	4.61999i	1.35300	+	1.78028i	−1.37762	−	1.08603i	2.89751	−	2.67843i	3.61523	−	5.89952i	−2.53133	+	0.199220i	0.329128	−	5.76884i
24.6	−1.94343	−	1.65984i	3.08083	−	0.121046i	0.708959	+	4.47619i	0.156641	+	2.23057i	−6.18829	−	4.87846i	−2.62183	+	2.42359i	3.38119	−	5.51760i	6.48613	−	0.510469i	3.39798	−	4.59496i
24.7	−1.91514	−	1.63568i	1.58564	−	0.0623001i	0.679431	+	4.28976i	−2.07280	−	0.838756i	−3.13864	−	2.47430i	−2.68305	+	2.48018i	3.08358	−	5.03194i	−0.480364	+	0.0378055i	2.59776	+	4.99678i
24.8	−1.89233	−	1.61620i	−3.17242	+	0.124645i	0.655931	+	4.14139i	−1.02327	+	1.98820i	6.20470	+	4.89139i	2.76645	−	2.55728i	2.85152	−	4.65326i	7.05793	−	0.555471i	5.14968	−	2.10851i
24.9	−1.87593	−	1.60220i	−2.28325	+	0.0897093i	0.639218	+	4.03586i	−1.83246	−	1.28144i	4.42696	+	3.48994i	−0.881491	+	0.814842i	2.68910	−	4.38821i	2.21444	−	0.174281i	1.38445	+	5.33986i
24.10	−1.81411	−	1.54940i	−1.66293	+	0.0653365i	0.577501	+	3.64619i	1.49196	+	1.66555i	3.11797	+	2.45801i	−2.07688	+	1.91985i	2.10869	−	3.44107i	−0.229698	+	0.0180776i	−0.125976	−	5.33314i
24.11	−1.80696	−	1.54329i	0.283569	−	0.0111414i	0.570492	+	3.60195i	0.402620	−	2.19952i	−0.529592	−	0.417497i	1.62864	−	1.50550i	2.04475	−	3.33673i	−2.91046	+	0.229059i	−4.12202	+	3.35309i
24.12	−1.76226	−	1.50511i	1.27925	−	0.0502620i	0.527327	+	3.32941i	2.21755	+	0.287186i	−2.33003	−	1.83684i	−2.43201	+	2.24813i	1.66004	−	2.70894i	−1.35679	+	0.106782i	−3.47565	−	3.84375i
24.13	−1.72711	−	1.47509i	−1.21237	+	0.0476343i	0.494146	+	3.11991i	−1.38873	−	1.75255i	2.16417	+	1.70609i	2.41982	−	2.23686i	1.37521	−	2.24414i	−1.52317	+	0.119876i	−0.186681	+	5.07535i
24.14	−1.68136	−	1.43602i	1.66984	−	0.0656083i	0.451960	+	2.85356i	−2.15359	+	0.601705i	−2.90183	−	2.28762i	0.993624	−	0.918497i	1.02723	−	1.67628i	−0.206679	+	0.0162660i	4.48503	+	2.08091i
24.15	−1.65240	−	1.41129i	2.45355	−	0.0964002i	0.425840	+	2.68864i	2.21379	−	0.314861i	−4.19030	−	3.30337i	1.64370	−	1.51942i	0.819952	−	1.33804i	3.01986	−	0.237668i	−4.10243	−	2.60401i
24.16	−1.60518	−	1.37096i	−1.38041	+	0.0542364i	0.384225	+	2.42590i	−1.66034	+	1.49775i	2.29017	+	1.80542i	1.93224	−	1.78614i	0.503113	−	0.821006i	−1.08817	+	0.0856406i	4.71851	−	0.127917i
24.17	−1.55841	−	1.33101i	2.30474	−	0.0905535i	0.344193	+	2.17315i	1.06967	−	1.96362i	−3.71227	−	2.92651i	−1.03228	+	0.954230i	0.214422	−	0.349905i	2.31288	−	0.182028i	−4.28059	+	1.63638i
24.18	−1.54264	−	1.31754i	−2.15875	+	0.0848174i	0.330960	+	2.08960i	−2.23379	−	0.101007i	3.44192	+	2.71339i	−2.74501	+	2.53746i	0.122585	−	0.200040i	1.66224	−	0.130821i	3.31285	+	3.09892i
24.19	−1.48084	−	1.26476i	−0.0635833	+	0.00249820i	0.280411	+	1.77044i	−0.827015	+	2.07751i	0.0973165	+	0.0767182i	−2.82505	+	2.61145i	−0.211126	+	0.344526i	−2.98672	+	0.235060i	3.85223	−	2.03049i
24.20	−1.46677	−	1.25274i	2.70244	−	0.106179i	0.269186	+	1.69957i	0.307848	+	2.21478i	−4.09686	−	3.22970i	2.51987	−	2.32934i	−0.281439	+	0.459267i	4.30113	−	0.338507i	2.32299	−	3.63421i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
11.d	odd	10	1	inner
17.e	odd	16	1	inner
55.h	odd	10	1	inner
85.p	odd	16	1	inner
187.t	even	80	1	inner
935.cp	even	80	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	935.2.cp.a	✓	3328
5.b	even	2	1	inner	935.2.cp.a	✓	3328
11.d	odd	10	1	inner	935.2.cp.a	✓	3328
17.e	odd	16	1	inner	935.2.cp.a	✓	3328
55.h	odd	10	1	inner	935.2.cp.a	✓	3328
85.p	odd	16	1	inner	935.2.cp.a	✓	3328
187.t	even	80	1	inner	935.2.cp.a	✓	3328
935.cp	even	80	1	inner	935.2.cp.a	✓	3328

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
935.2.cp.a	✓	3328	1.a	even	1	1	trivial
935.2.cp.a	✓	3328	5.b	even	2	1	inner
935.2.cp.a	✓	3328	11.d	odd	10	1	inner
935.2.cp.a	✓	3328	17.e	odd	16	1	inner
935.2.cp.a	✓	3328	55.h	odd	10	1	inner
935.2.cp.a	✓	3328	85.p	odd	16	1	inner
935.2.cp.a	✓	3328	187.t	even	80	1	inner
935.2.cp.a	✓	3328	935.cp	even	80	1	inner

Hecke kernels

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