Newform orbit 1020.3.bc.a

• Label: 1020.3.bc.a
• Level: $1020$
• Weight: $3$
• Character orbit: 1020.bc
• Analytic conductor: $27.793$
• Analytic rank: $0$
• Dimension: $96$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1020.bc (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(27.7929869648\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(48\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q - 8 q^{3}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
701.1		0		−2.99983	−	0.0319133i		0		1.58114	+	1.58114i		0		−2.18976	−	2.18976i		0		8.99796	+	0.191469i		0
701.2		0		−2.99006	+	0.243979i		0		−1.58114	−	1.58114i		0		8.18085	+	8.18085i		0		8.88095	−	1.45903i		0
701.3		0		−2.96619	+	0.449113i		0		1.58114	+	1.58114i		0		3.25780	+	3.25780i		0		8.59659	−	2.66431i		0
701.4		0		−2.91510	+	0.708668i		0		−1.58114	−	1.58114i		0		−3.70850	−	3.70850i		0		7.99558	−	4.13167i		0
701.5		0		−2.87769	−	0.847873i		0		−1.58114	−	1.58114i		0		−3.23891	−	3.23891i		0		7.56222	+	4.87983i		0
701.6		0		−2.81027	+	1.04993i		0		1.58114	+	1.58114i		0		1.89809	+	1.89809i		0		6.79529	−	5.90119i		0
701.7		0		−2.75507	+	1.18727i		0		−1.58114	−	1.58114i		0		7.37174	+	7.37174i		0		6.18077	−	6.54202i		0
701.8		0		−2.68472	−	1.33875i		0		−1.58114	−	1.58114i		0		−1.29188	−	1.29188i		0		5.41548	+	7.18836i		0
701.9		0		−2.67349	+	1.36106i		0		−1.58114	−	1.58114i		0		−6.29057	−	6.29057i		0		5.29505	−	7.27753i		0
701.10		0		−2.55652	−	1.56977i		0		1.58114	+	1.58114i		0		7.74236	+	7.74236i		0		4.07163	+	8.02632i		0
701.11		0		−2.43789	−	1.74834i		0		1.58114	+	1.58114i		0		−8.85638	−	8.85638i		0		2.88662	+	8.52452i		0
701.12		0		−2.23015	−	2.00659i		0		1.58114	+	1.58114i		0		4.31939	+	4.31939i		0		0.947174	+	8.95002i		0
701.13		0		−2.20967	+	2.02913i		0		−1.58114	−	1.58114i		0		−7.12660	−	7.12660i		0		0.765285	−	8.96740i		0
701.14		0		−2.02913	+	2.20967i		0		1.58114	+	1.58114i		0		−7.12660	−	7.12660i		0		−0.765285	−	8.96740i		0
701.15		0		−1.47457	−	2.61259i		0		−1.58114	−	1.58114i		0		6.29143	+	6.29143i		0		−4.65126	+	7.70492i		0
701.16		0		−1.36106	+	2.67349i		0		1.58114	+	1.58114i		0		−6.29057	−	6.29057i		0		−5.29505	−	7.27753i		0
701.17		0		−1.23515	−	2.73394i		0		1.58114	+	1.58114i		0		−3.40115	−	3.40115i		0		−5.94881	+	6.75364i		0
701.18		0		−1.18727	+	2.75507i		0		1.58114	+	1.58114i		0		7.37174	+	7.37174i		0		−6.18077	−	6.54202i		0
701.19		0		−1.14814	−	2.77160i		0		−1.58114	−	1.58114i		0		−1.23665	−	1.23665i		0		−6.36355	+	6.36437i		0
701.20		0		−1.04993	+	2.81027i		0		−1.58114	−	1.58114i		0		1.89809	+	1.89809i		0		−6.79529	−	5.90119i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
17.c	even	4	1	inner
51.f	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1020.3.bc.a	✓	96
3.b	odd	2	1	inner	1020.3.bc.a	✓	96
17.c	even	4	1	inner	1020.3.bc.a	✓	96
51.f	odd	4	1	inner	1020.3.bc.a	✓	96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1020.3.bc.a	✓	96	1.a	even	1	1	trivial
1020.3.bc.a	✓	96	3.b	odd	2	1	inner
1020.3.bc.a	✓	96	17.c	even	4	1	inner
1020.3.bc.a	✓	96	51.f	odd	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(1020, [\chi])\).