Newform orbit 1014.2.g.e

• Label: 1014.2.g.e
• Level: $1014$
• Weight: $2$
• Character orbit: 1014.g
• Analytic conductor: $8.097$
• Analytic rank: $0$
• Dimension: $48$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.09683076496\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(24\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 4 q^{3} + 20 q^{9} - 48 q^{16} - 32 q^{22} + 116 q^{27} + 8 q^{40} - 40 q^{42} + 4 q^{48} - 144 q^{55} - 80 q^{61} + 96 q^{66} - 56 q^{79} + 84 q^{81} + 224 q^{87} - 16 q^{94}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
239.1	−0.707107	−	0.707107i	−1.68568	+	0.398108i			1.00000i	2.32916	+	2.32916i	1.47346	+	0.910449i	−2.38633	−	2.38633i	0.707107	−	0.707107i	2.68302	−	1.34216i		−	3.29393i
239.2	−0.707107	−	0.707107i	−1.13362	−	1.30955i			1.00000i	−0.0594916	−	0.0594916i	−0.124399	+	1.72758i	−3.26082	−	3.26082i	0.707107	−	0.707107i	−0.429819	+	2.96905i			0.0841338i
239.3	−0.707107	−	0.707107i	−0.257671	+	1.71278i			1.00000i	2.81946	+	2.81946i	1.39332	−	1.02892i	−0.454181	−	0.454181i	0.707107	−	0.707107i	−2.86721	−	0.882666i		−	3.98732i
239.4	−0.707107	−	0.707107i	1.58955	+	0.688001i			1.00000i	−0.822256	−	0.822256i	−0.637488	−	1.61047i	−1.88206	−	1.88206i	0.707107	−	0.707107i	2.05331	+	2.18722i			1.16285i
239.5	−0.707107	−	0.707107i	−0.739750	+	1.56613i			1.00000i	−2.01447	−	2.01447i	1.63050	−	0.584341i	−2.99993	−	2.99993i	0.707107	−	0.707107i	−1.90554	−	2.31709i			2.84889i
239.6	−0.707107	−	0.707107i	−1.68568	−	0.398108i			1.00000i	2.32916	+	2.32916i	0.910449	+	1.47346i	2.38633	+	2.38633i	0.707107	−	0.707107i	2.68302	+	1.34216i		−	3.29393i
239.7	−0.707107	−	0.707107i	1.72717	+	0.129918i			1.00000i	−1.54530	−	1.54530i	−1.12943	−	1.31316i	−0.651496	−	0.651496i	0.707107	−	0.707107i	2.96624	+	0.448782i			2.18538i
239.8	−0.707107	−	0.707107i	−0.257671	−	1.71278i			1.00000i	2.81946	+	2.81946i	−1.02892	+	1.39332i	0.454181	+	0.454181i	0.707107	−	0.707107i	−2.86721	+	0.882666i		−	3.98732i
239.9	−0.707107	−	0.707107i	1.72717	−	0.129918i			1.00000i	−1.54530	−	1.54530i	−1.31316	−	1.12943i	0.651496	+	0.651496i	0.707107	−	0.707107i	2.96624	−	0.448782i			2.18538i
239.10	−0.707107	−	0.707107i	1.58955	−	0.688001i			1.00000i	−0.822256	−	0.822256i	−1.61047	−	0.637488i	1.88206	+	1.88206i	0.707107	−	0.707107i	2.05331	−	2.18722i			1.16285i
239.11	−0.707107	−	0.707107i	−1.13362	+	1.30955i			1.00000i	−0.0594916	−	0.0594916i	1.72758	−	0.124399i	3.26082	+	3.26082i	0.707107	−	0.707107i	−0.429819	−	2.96905i			0.0841338i
239.12	−0.707107	−	0.707107i	−0.739750	−	1.56613i			1.00000i	−2.01447	−	2.01447i	−0.584341	+	1.63050i	2.99993	+	2.99993i	0.707107	−	0.707107i	−1.90554	+	2.31709i			2.84889i
239.13	0.707107	+	0.707107i	−0.739750	−	1.56613i			1.00000i	2.01447	+	2.01447i	0.584341	−	1.63050i	−2.99993	−	2.99993i	−0.707107	+	0.707107i	−1.90554	+	2.31709i			2.84889i
239.14	0.707107	+	0.707107i	−1.13362	+	1.30955i			1.00000i	0.0594916	+	0.0594916i	−1.72758	+	0.124399i	−3.26082	−	3.26082i	−0.707107	+	0.707107i	−0.429819	−	2.96905i			0.0841338i
239.15	0.707107	+	0.707107i	1.58955	−	0.688001i			1.00000i	0.822256	+	0.822256i	1.61047	+	0.637488i	−1.88206	−	1.88206i	−0.707107	+	0.707107i	2.05331	−	2.18722i			1.16285i
239.16	0.707107	+	0.707107i	1.72717	−	0.129918i			1.00000i	1.54530	+	1.54530i	1.31316	+	1.12943i	−0.651496	−	0.651496i	−0.707107	+	0.707107i	2.96624	−	0.448782i			2.18538i
239.17	0.707107	+	0.707107i	−0.257671	−	1.71278i			1.00000i	−2.81946	−	2.81946i	1.02892	−	1.39332i	−0.454181	−	0.454181i	−0.707107	+	0.707107i	−2.86721	+	0.882666i		−	3.98732i
239.18	0.707107	+	0.707107i	1.72717	+	0.129918i			1.00000i	1.54530	+	1.54530i	1.12943	+	1.31316i	0.651496	+	0.651496i	−0.707107	+	0.707107i	2.96624	+	0.448782i			2.18538i
239.19	0.707107	+	0.707107i	−1.68568	−	0.398108i			1.00000i	−2.32916	−	2.32916i	−0.910449	−	1.47346i	−2.38633	−	2.38633i	−0.707107	+	0.707107i	2.68302	+	1.34216i		−	3.29393i
239.20	0.707107	+	0.707107i	−0.739750	+	1.56613i			1.00000i	2.01447	+	2.01447i	−1.63050	+	0.584341i	2.99993	+	2.99993i	−0.707107	+	0.707107i	−1.90554	−	2.31709i			2.84889i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
13.b	even	2	1	inner
13.d	odd	4	2	inner
39.d	odd	2	1	inner
39.f	even	4	2	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1014.2.g.e	✓	48
3.b	odd	2	1	inner	1014.2.g.e	✓	48
13.b	even	2	1	inner	1014.2.g.e	✓	48
13.d	odd	4	2	inner	1014.2.g.e	✓	48
39.d	odd	2	1	inner	1014.2.g.e	✓	48
39.f	even	4	2	inner	1014.2.g.e	✓	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1014.2.g.e	✓	48	1.a	even	1	1	trivial
1014.2.g.e	✓	48	3.b	odd	2	1	inner
1014.2.g.e	✓	48	13.b	even	2	1	inner
1014.2.g.e	✓	48	13.d	odd	4	2	inner
1014.2.g.e	✓	48	39.d	odd	2	1	inner
1014.2.g.e	✓	48	39.f	even	4	2	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1014, [\chi])\):

\( T_{5}^{24} + 461T_{5}^{20} + 64954T_{5}^{16} + 3312721T_{5}^{12} + 50551376T_{5}^{8} + 81750528T_{5}^{4} + 4096 \)

\( T_{7}^{24} + 957T_{7}^{20} + 293514T_{7}^{16} + 31671457T_{7}^{12} + 981804448T_{7}^{8} + 853511424T_{7}^{4} + 116985856 \)