Newform orbit 460.2.g.c

• Label: 460.2.g.c
• Level: $460$
• Weight: $2$
• Character orbit: 460.g
• Analytic conductor: $3.673$
• Analytic rank: $0$
• Dimension: $56$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.67311849298\)
Analytic rank:	\(0\)
Dimension:	\(56\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
459.1	−1.35976	−	0.388659i	1.11016			1.69789	+	1.05697i	−1.71804	+	1.43120i	−1.50955	−	0.431474i		−	4.32159i	−1.89792	−	2.09712i	−1.76755			2.89237	−	1.27835i
459.2	−1.35976	−	0.388659i	1.11016			1.69789	+	1.05697i	1.71804	−	1.43120i	−1.50955	−	0.431474i			4.32159i	−1.89792	−	2.09712i	−1.76755			−2.89237	+	1.27835i
459.3	−1.35976	+	0.388659i	1.11016			1.69789	−	1.05697i	−1.71804	−	1.43120i	−1.50955	+	0.431474i			4.32159i	−1.89792	+	2.09712i	−1.76755			2.89237	+	1.27835i
459.4	−1.35976	+	0.388659i	1.11016			1.69789	−	1.05697i	1.71804	+	1.43120i	−1.50955	+	0.431474i		−	4.32159i	−1.89792	+	2.09712i	−1.76755			−2.89237	−	1.27835i
459.5	−1.28797	−	0.584066i	2.56426			1.31773	+	1.50452i	−0.662839	−	2.13557i	−3.30269	−	1.49770i		−	1.62105i	−0.818466	−	2.70742i	3.57544			−0.393594	+	3.13769i
459.6	−1.28797	−	0.584066i	2.56426			1.31773	+	1.50452i	0.662839	+	2.13557i	−3.30269	−	1.49770i			1.62105i	−0.818466	−	2.70742i	3.57544			0.393594	−	3.13769i
459.7	−1.28797	+	0.584066i	2.56426			1.31773	−	1.50452i	−0.662839	+	2.13557i	−3.30269	+	1.49770i			1.62105i	−0.818466	+	2.70742i	3.57544			−0.393594	−	3.13769i
459.8	−1.28797	+	0.584066i	2.56426			1.31773	−	1.50452i	0.662839	−	2.13557i	−3.30269	+	1.49770i		−	1.62105i	−0.818466	+	2.70742i	3.57544			0.393594	+	3.13769i
459.9	−1.20833	−	0.734800i	−1.77158			0.920137	+	1.77577i	−1.90499	−	1.17090i	2.14066	+	1.30176i			1.27817i	0.193001	−	2.82183i	0.138505			1.44148	+	2.81463i
459.10	−1.20833	−	0.734800i	−1.77158			0.920137	+	1.77577i	1.90499	+	1.17090i	2.14066	+	1.30176i		−	1.27817i	0.193001	−	2.82183i	0.138505			−1.44148	−	2.81463i
459.11	−1.20833	+	0.734800i	−1.77158			0.920137	−	1.77577i	−1.90499	+	1.17090i	2.14066	−	1.30176i		−	1.27817i	0.193001	+	2.82183i	0.138505			1.44148	−	2.81463i
459.12	−1.20833	+	0.734800i	−1.77158			0.920137	−	1.77577i	1.90499	−	1.17090i	2.14066	−	1.30176i			1.27817i	0.193001	+	2.82183i	0.138505			−1.44148	+	2.81463i
459.13	−0.968186	−	1.03083i	0.281229			−0.125231	+	1.99608i	−1.92344	+	1.14033i	−0.272282	−	0.289900i			0.654652i	2.17887	−	1.80348i	−2.92091			3.03775	+	0.878693i
459.14	−0.968186	−	1.03083i	0.281229			−0.125231	+	1.99608i	1.92344	−	1.14033i	−0.272282	−	0.289900i		−	0.654652i	2.17887	−	1.80348i	−2.92091			−3.03775	−	0.878693i
459.15	−0.968186	+	1.03083i	0.281229			−0.125231	−	1.99608i	−1.92344	−	1.14033i	−0.272282	+	0.289900i		−	0.654652i	2.17887	+	1.80348i	−2.92091			3.03775	−	0.878693i
459.16	−0.968186	+	1.03083i	0.281229			−0.125231	−	1.99608i	1.92344	+	1.14033i	−0.272282	+	0.289900i			0.654652i	2.17887	+	1.80348i	−2.92091			−3.03775	+	0.878693i
459.17	−0.627129	−	1.26756i	−3.03928			−1.21342	+	1.58985i	−0.951754	+	2.02340i	1.90602	+	3.85247i			1.96560i	2.77620	+	0.541043i	6.23720			3.16166	−	0.0625285i
459.18	−0.627129	−	1.26756i	−3.03928			−1.21342	+	1.58985i	0.951754	−	2.02340i	1.90602	+	3.85247i		−	1.96560i	2.77620	+	0.541043i	6.23720			−3.16166	+	0.0625285i
459.19	−0.627129	+	1.26756i	−3.03928			−1.21342	−	1.58985i	−0.951754	−	2.02340i	1.90602	−	3.85247i		−	1.96560i	2.77620	−	0.541043i	6.23720			3.16166	+	0.0625285i
459.20	−0.627129	+	1.26756i	−3.03928			−1.21342	−	1.58985i	0.951754	+	2.02340i	1.90602	−	3.85247i			1.96560i	2.77620	−	0.541043i	6.23720			−3.16166	−	0.0625285i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
5.b	even	2	1	inner
20.d	odd	2	1	inner
23.b	odd	2	1	inner
92.b	even	2	1	inner
115.c	odd	2	1	inner
460.g	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	460.2.g.c	✓	56
4.b	odd	2	1	inner	460.2.g.c	✓	56
5.b	even	2	1	inner	460.2.g.c	✓	56
20.d	odd	2	1	inner	460.2.g.c	✓	56
23.b	odd	2	1	inner	460.2.g.c	✓	56
92.b	even	2	1	inner	460.2.g.c	✓	56
115.c	odd	2	1	inner	460.2.g.c	✓	56
460.g	even	2	1	inner	460.2.g.c	✓	56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
460.2.g.c	✓	56	1.a	even	1	1	trivial
460.2.g.c	✓	56	4.b	odd	2	1	inner
460.2.g.c	✓	56	5.b	even	2	1	inner
460.2.g.c	✓	56	20.d	odd	2	1	inner
460.2.g.c	✓	56	23.b	odd	2	1	inner
460.2.g.c	✓	56	92.b	even	2	1	inner
460.2.g.c	✓	56	115.c	odd	2	1	inner
460.2.g.c	✓	56	460.g	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{14} - 23T_{3}^{12} + 191T_{3}^{10} - 712T_{3}^{8} + 1213T_{3}^{6} - 805T_{3}^{4} + 107T_{3}^{2} - 4 \) acting on \(S_{2}^{\mathrm{new}}(460, [\chi])\).