Newform orbit 920.2.bn.a

• Label: 920.2.bn.a
• Level: $920$
• Weight: $2$
• Character orbit: 920.bn
• Analytic conductor: $7.346$
• Analytic rank: $0$
• Dimension: $40$
• CM discriminant: -40
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bn (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.34623698596\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(4\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 8 q^{4} - 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−0.587486	−	1.28641i		0		−1.30972	+	1.51150i	−1.20891	+	1.88110i		0		−0.707757	+	0.101760i	2.71386	+	0.796860i	2.52376	−	1.62192i	3.13009	+	0.450039i
19.2	−0.587486	−	1.28641i		0		−1.30972	+	1.51150i	1.20891	−	1.88110i		0		−4.38552	+	0.630543i	2.71386	+	0.796860i	2.52376	−	1.62192i	−3.13009	−	0.450039i
19.3	0.587486	+	1.28641i		0		−1.30972	+	1.51150i	−1.20891	+	1.88110i		0		4.38552	−	0.630543i	−2.71386	−	0.796860i	2.52376	−	1.62192i	−3.13009	−	0.450039i
19.4	0.587486	+	1.28641i		0		−1.30972	+	1.51150i	1.20891	−	1.88110i		0		0.707757	−	0.101760i	−2.71386	−	0.796860i	2.52376	−	1.62192i	3.13009	+	0.450039i
99.1	−0.926113	+	1.06879i		0		−0.284630	−	1.97964i	−2.03400	+	0.928896i		0		0.222863	+	0.759001i	2.37942	+	1.52916i	1.24625	−	2.72890i	0.890917	−	3.03418i
99.2	−0.926113	+	1.06879i		0		−0.284630	−	1.97964i	2.03400	−	0.928896i		0		−1.42732	−	4.86099i	2.37942	+	1.52916i	1.24625	−	2.72890i	−0.890917	+	3.03418i
99.3	0.926113	−	1.06879i		0		−0.284630	−	1.97964i	−2.03400	+	0.928896i		0		1.42732	+	4.86099i	−2.37942	−	1.52916i	1.24625	−	2.72890i	−0.890917	+	3.03418i
99.4	0.926113	−	1.06879i		0		−0.284630	−	1.97964i	2.03400	−	0.928896i		0		−0.222863	−	0.759001i	−2.37942	−	1.52916i	1.24625	−	2.72890i	0.890917	−	3.03418i
339.1	−0.587486	+	1.28641i		0		−1.30972	−	1.51150i	−1.20891	−	1.88110i		0		−0.707757	−	0.101760i	2.71386	−	0.796860i	2.52376	+	1.62192i	3.13009	−	0.450039i
339.2	−0.587486	+	1.28641i		0		−1.30972	−	1.51150i	1.20891	+	1.88110i		0		−4.38552	−	0.630543i	2.71386	−	0.796860i	2.52376	+	1.62192i	−3.13009	+	0.450039i
339.3	0.587486	−	1.28641i		0		−1.30972	−	1.51150i	−1.20891	−	1.88110i		0		4.38552	+	0.630543i	−2.71386	+	0.796860i	2.52376	+	1.62192i	−3.13009	+	0.450039i
339.4	0.587486	−	1.28641i		0		−1.30972	−	1.51150i	1.20891	+	1.88110i		0		0.707757	+	0.101760i	−2.71386	+	0.796860i	2.52376	+	1.62192i	3.13009	−	0.450039i
379.1	−1.18971	+	0.764582i		0		0.830830	−	1.81926i	−0.629973	−	2.14549i		0		3.99895	−	3.46511i	0.402527	+	2.79964i	−2.87848	−	0.845198i	2.38989	+	2.07085i
379.2	−1.18971	+	0.764582i		0		0.830830	−	1.81926i	0.629973	+	2.14549i		0		−1.68762	+	1.46233i	0.402527	+	2.79964i	−2.87848	−	0.845198i	−2.38989	−	2.07085i
379.3	1.18971	−	0.764582i		0		0.830830	−	1.81926i	−0.629973	−	2.14549i		0		1.68762	−	1.46233i	−0.402527	−	2.79964i	−2.87848	−	0.845198i	−2.38989	−	2.07085i
379.4	1.18971	−	0.764582i		0		0.830830	−	1.81926i	0.629973	+	2.14549i		0		−3.99895	+	3.46511i	−0.402527	−	2.79964i	−2.87848	−	0.845198i	2.38989	+	2.07085i
419.1	−1.35693	−	0.398430i		0		1.68251	+	1.08128i	−2.21331	−	0.318226i		0		4.62806	−	2.11357i	−1.85223	−	2.13758i	−0.426945	−	2.96946i	2.87651	+	1.31366i
419.2	−1.35693	−	0.398430i		0		1.68251	+	1.08128i	2.21331	+	0.318226i		0		−3.17837	+	1.45151i	−1.85223	−	2.13758i	−0.426945	−	2.96946i	−2.87651	−	1.31366i
419.3	1.35693	+	0.398430i		0		1.68251	+	1.08128i	−2.21331	−	0.318226i		0		3.17837	−	1.45151i	1.85223	+	2.13758i	−0.426945	−	2.96946i	−2.87651	−	1.31366i
419.4	1.35693	+	0.398430i		0		1.68251	+	1.08128i	2.21331	+	0.318226i		0		−4.62806	+	2.11357i	1.85223	+	2.13758i	−0.426945	−	2.96946i	2.87651	+	1.31366i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
40.e	odd	2	1	CM by \(\Q(\sqrt{-10}) \)
5.b	even	2	1	inner
8.d	odd	2	1	inner
23.d	odd	22	1	inner
115.i	odd	22	1	inner
184.j	even	22	1	inner
920.bn	even	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	920.2.bn.a	✓	40
5.b	even	2	1	inner	920.2.bn.a	✓	40
8.d	odd	2	1	inner	920.2.bn.a	✓	40
23.d	odd	22	1	inner	920.2.bn.a	✓	40
40.e	odd	2	1	CM	920.2.bn.a	✓	40
115.i	odd	22	1	inner	920.2.bn.a	✓	40
184.j	even	22	1	inner	920.2.bn.a	✓	40
920.bn	even	22	1	inner	920.2.bn.a	✓	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
920.2.bn.a	✓	40	1.a	even	1	1	trivial
920.2.bn.a	✓	40	5.b	even	2	1	inner
920.2.bn.a	✓	40	8.d	odd	2	1	inner
920.2.bn.a	✓	40	23.d	odd	22	1	inner
920.2.bn.a	✓	40	40.e	odd	2	1	CM
920.2.bn.a	✓	40	115.i	odd	22	1	inner
920.2.bn.a	✓	40	184.j	even	22	1	inner
920.2.bn.a	✓	40	920.bn	even	22	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} \) acting on \(S_{2}^{\mathrm{new}}(920, [\chi])\).