Newform orbit 935.2.bp.a

• Label: 935.2.bp.a
• Level: $935$
• Weight: $2$
• Character orbit: 935.bp
• Analytic conductor: $7.466$
• Analytic rank: $0$
• Dimension: $64$
• CM discriminant: -55
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.bp (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.46601258899\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(8\) over \(\Q(\zeta_{16})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{16}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 64 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
54.1	−2.61312	+	1.08239i		0		4.24262	−	4.24262i	−1.24229	−	1.85922i		0		0.947908	−	1.41864i	−4.32952	+	10.4524i	2.77164	+	1.14805i	5.25866	+	3.51373i
54.2	−2.16972	+	0.898726i		0		2.48575	−	2.48575i	1.24229	+	1.85922i		0		−1.78717	+	2.67469i	−1.36191	+	3.28795i	2.77164	+	1.14805i	−4.36636	−	2.91751i
54.3	−1.45628	+	0.603212i		0		0.342678	−	0.342678i	−1.24229	−	1.85922i		0		2.33419	−	3.49336i	0.914095	−	2.20682i	2.77164	+	1.14805i	2.93063	+	1.95819i
54.4	−0.00542374	+	0.00224659i		0		−1.41419	+	1.41419i	1.24229	+	1.85922i		0		2.78279	−	4.16473i	0.00898627	−	0.0216948i	2.77164	+	1.14805i	−0.0109148	−	0.00729302i
54.5	0.00542374	−	0.00224659i		0		−1.41419	+	1.41419i	1.24229	+	1.85922i		0		−2.78279	+	4.16473i	−0.00898627	+	0.0216948i	2.77164	+	1.14805i	0.0109148	+	0.00729302i
54.6	1.45628	−	0.603212i		0		0.342678	−	0.342678i	−1.24229	−	1.85922i		0		−2.33419	+	3.49336i	−0.914095	+	2.20682i	2.77164	+	1.14805i	−2.93063	−	1.95819i
54.7	2.16972	−	0.898726i		0		2.48575	−	2.48575i	1.24229	+	1.85922i		0		1.78717	−	2.67469i	1.36191	−	3.28795i	2.77164	+	1.14805i	4.36636	+	2.91751i
54.8	2.61312	−	1.08239i		0		4.24262	−	4.24262i	−1.24229	−	1.85922i		0		−0.947908	+	1.41864i	4.32952	−	10.4524i	2.77164	+	1.14805i	−5.25866	−	3.51373i
109.1	−1.06115	+	2.56185i		0		−4.02282	−	4.02282i	−0.436235	−	2.19310i		0		0.893470	−	4.49178i	9.45101	−	3.91474i	−1.14805	−	2.77164i	6.08132	+	1.20965i
109.2	−0.999138	+	2.41213i		0		−3.40589	−	3.40589i	0.436235	+	2.19310i		0		−0.681476	+	3.42601i	6.79416	−	2.81423i	−1.14805	−	2.77164i	−5.72591	−	1.13896i
109.3	−0.416288	+	1.00501i		0		0.577467	+	0.577467i	−0.436235	−	2.19310i		0		−0.775421	+	3.89830i	−2.83077	+	1.17254i	−1.14805	−	2.77164i	2.38569	+	0.474543i
109.4	−0.213367	+	0.515114i		0		1.19440	+	1.19440i	0.436235	+	2.19310i		0		−0.517105	+	2.59966i	−1.90032	+	0.787140i	−1.14805	−	2.77164i	−1.22278	−	0.243225i
109.5	0.213367	−	0.515114i		0		1.19440	+	1.19440i	0.436235	+	2.19310i		0		0.517105	−	2.59966i	1.90032	−	0.787140i	−1.14805	−	2.77164i	1.22278	+	0.243225i
109.6	0.416288	−	1.00501i		0		0.577467	+	0.577467i	−0.436235	−	2.19310i		0		0.775421	−	3.89830i	2.83077	−	1.17254i	−1.14805	−	2.77164i	−2.38569	−	0.474543i
109.7	0.999138	−	2.41213i		0		−3.40589	−	3.40589i	0.436235	+	2.19310i		0		0.681476	−	3.42601i	−6.79416	+	2.81423i	−1.14805	−	2.77164i	5.72591	+	1.13896i
109.8	1.06115	−	2.56185i		0		−4.02282	−	4.02282i	−0.436235	−	2.19310i		0		−0.893470	+	4.49178i	−9.45101	+	3.91474i	−1.14805	−	2.77164i	−6.08132	−	1.20965i
164.1	−2.56397	−	1.06203i		0		4.03181	+	4.03181i	−1.85922	−	1.24229i		0		−4.36147	+	2.91424i	−3.93147	−	9.49140i	−2.77164	+	1.14805i	3.44763	+	5.15975i
164.2	−1.85159	−	0.766954i		0		1.42595	+	1.42595i	−1.85922	−	1.24229i		0		1.94178	−	1.29746i	−0.0127349	−	0.0307449i	−2.77164	+	1.14805i	2.48974	+	3.72616i
164.3	−1.84392	−	0.763777i		0		1.40247	+	1.40247i	1.85922	+	1.24229i		0		3.94805	−	2.63800i	0.0126822	+	0.0306175i	−2.77164	+	1.14805i	−2.47942	−	3.71072i
164.4	−0.504475	−	0.208960i		0		−1.20338	−	1.20338i	1.85922	+	1.24229i		0		−0.578886	+	0.386800i	0.773538	+	1.86749i	−2.77164	+	1.14805i	−0.678341	−	1.01521i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
55.d	odd	2	1	CM by \(\Q(\sqrt{-55}) \)
5.b	even	2	1	inner
11.b	odd	2	1	inner
17.e	odd	16	1	inner
85.p	odd	16	1	inner
187.m	even	16	1	inner
935.bp	even	16	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	935.2.bp.a	✓	64
5.b	even	2	1	inner	935.2.bp.a	✓	64
11.b	odd	2	1	inner	935.2.bp.a	✓	64
17.e	odd	16	1	inner	935.2.bp.a	✓	64
55.d	odd	2	1	CM	935.2.bp.a	✓	64
85.p	odd	16	1	inner	935.2.bp.a	✓	64
187.m	even	16	1	inner	935.2.bp.a	✓	64
935.bp	even	16	1	inner	935.2.bp.a	✓	64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
935.2.bp.a	✓	64	1.a	even	1	1	trivial
935.2.bp.a	✓	64	5.b	even	2	1	inner
935.2.bp.a	✓	64	11.b	odd	2	1	inner
935.2.bp.a	✓	64	17.e	odd	16	1	inner
935.2.bp.a	✓	64	55.d	odd	2	1	CM
935.2.bp.a	✓	64	85.p	odd	16	1	inner
935.2.bp.a	✓	64	187.m	even	16	1	inner
935.2.bp.a	✓	64	935.bp	even	16	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^64 + 8960*T2^56 + 1472*T2^54 - 153088*T2^50 + 26961920*T2^48 + 1978368*T2^46 + 1083392*T2^44 - 641368064*T2^42 + 31115673600*T2^40 - 15474254272*T2^38 + 4922933248*T2^36 - 328422171136*T2^34 + 13013173142082*T2^32 - 15139419856896*T2^30 + 4044811530240*T2^28 + 134490823786496*T2^26 + 850426401714944*T2^24 - 105791569560128*T2^22 + 371279027765248*T2^20 + 5426044508846592*T2^18 + 15677807782406144*T2^16 + 16244819318149120*T2^14 + 8467749473454080*T2^12 + 169888152584192*T2^10 + 108506170359808*T2^8 + 123529611748928*T2^6 + 70311204749312*T2^4 - 3427086848*T2^2 + 83521