Newform orbit 460.2.e.b

• Label: 460.2.e.b
• Level: $460$
• Weight: $2$
• Character orbit: 460.e
• Analytic conductor: $3.673$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(3.67311849298\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9 + 24 * q^12 - 4 * q^13 + 20 * q^16 - 56 * q^18 - 6 * q^24 - 32 * q^25 + 68 * q^26 + 8 * q^29 - 16 * q^32 + 8 * q^36 + 44 * q^41 - 4 * q^46 - 4 * q^48 - 12 * q^49 - 4 * q^50 + 16 * q^52 + 42 * q^54 - 10 * q^58 - 36 * q^62 - 22 * q^64 - 44 * q^69 - 42 * q^70 - 32 * q^72 - 8 * q^73 - 72 * q^77 + 122 * q^78 - 32 * q^81 + 20 * q^82 - 44 * q^85 + 64 * q^92 + 40 * q^93 - 26 * q^94 + 16 * q^96 + 62 * q^98

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
91.1	−1.39466	−	0.234385i		−	1.37989i	1.89013	+	0.653773i		−	1.00000i	−0.323424	+	1.92446i	−2.31854			−2.48284	−	1.35481i	1.09592			−0.234385	+	1.39466i
91.2	−1.39466	−	0.234385i		−	1.37989i	1.89013	+	0.653773i			1.00000i	−0.323424	+	1.92446i	2.31854			−2.48284	−	1.35481i	1.09592			0.234385	−	1.39466i
91.3	−1.39466	+	0.234385i			1.37989i	1.89013	−	0.653773i		−	1.00000i	−0.323424	−	1.92446i	2.31854			−2.48284	+	1.35481i	1.09592			0.234385	+	1.39466i
91.4	−1.39466	+	0.234385i			1.37989i	1.89013	−	0.653773i			1.00000i	−0.323424	−	1.92446i	−2.31854			−2.48284	+	1.35481i	1.09592			−0.234385	−	1.39466i
91.5	−1.05127	−	0.945957i		−	1.57817i	0.210332	+	1.98891i		−	1.00000i	−1.49288	+	1.65908i	1.14830			1.66031	−	2.28984i	0.509388			−0.945957	+	1.05127i
91.6	−1.05127	−	0.945957i		−	1.57817i	0.210332	+	1.98891i			1.00000i	−1.49288	+	1.65908i	−1.14830			1.66031	−	2.28984i	0.509388			0.945957	−	1.05127i
91.7	−1.05127	+	0.945957i			1.57817i	0.210332	−	1.98891i		−	1.00000i	−1.49288	−	1.65908i	−1.14830			1.66031	+	2.28984i	0.509388			0.945957	+	1.05127i
91.8	−1.05127	+	0.945957i			1.57817i	0.210332	−	1.98891i			1.00000i	−1.49288	−	1.65908i	1.14830			1.66031	+	2.28984i	0.509388			−0.945957	−	1.05127i
91.9	−0.265302	−	1.38911i		−	0.0612154i	−1.85923	+	0.737066i		−	1.00000i	−0.0850346	+	0.0162406i	0.810885			1.51712	+	2.38712i	2.99625			−1.38911	+	0.265302i
91.10	−0.265302	−	1.38911i		−	0.0612154i	−1.85923	+	0.737066i			1.00000i	−0.0850346	+	0.0162406i	−0.810885			1.51712	+	2.38712i	2.99625			1.38911	−	0.265302i
91.11	−0.265302	+	1.38911i			0.0612154i	−1.85923	−	0.737066i		−	1.00000i	−0.0850346	−	0.0162406i	−0.810885			1.51712	−	2.38712i	2.99625			1.38911	+	0.265302i
91.12	−0.265302	+	1.38911i			0.0612154i	−1.85923	−	0.737066i			1.00000i	−0.0850346	−	0.0162406i	0.810885			1.51712	−	2.38712i	2.99625			−1.38911	−	0.265302i
91.13	−0.151248	−	1.40610i		−	2.99817i	−1.95425	+	0.425339i		−	1.00000i	−4.21573	+	0.453465i	3.98264			0.893646	+	2.68354i	−5.98900			−1.40610	+	0.151248i
91.14	−0.151248	−	1.40610i		−	2.99817i	−1.95425	+	0.425339i			1.00000i	−4.21573	+	0.453465i	−3.98264			0.893646	+	2.68354i	−5.98900			1.40610	−	0.151248i
91.15	−0.151248	+	1.40610i			2.99817i	−1.95425	−	0.425339i		−	1.00000i	−4.21573	−	0.453465i	−3.98264			0.893646	−	2.68354i	−5.98900			1.40610	+	0.151248i
91.16	−0.151248	+	1.40610i			2.99817i	−1.95425	−	0.425339i			1.00000i	−4.21573	−	0.453465i	3.98264			0.893646	−	2.68354i	−5.98900			−1.40610	−	0.151248i
91.17	0.341935	−	1.37225i			2.41873i	−1.76616	−	0.938444i		−	1.00000i	3.31911	+	0.827049i	2.44077			−1.89170	+	2.10273i	−2.85025			−1.37225	−	0.341935i
91.18	0.341935	−	1.37225i			2.41873i	−1.76616	−	0.938444i			1.00000i	3.31911	+	0.827049i	−2.44077			−1.89170	+	2.10273i	−2.85025			1.37225	+	0.341935i
91.19	0.341935	+	1.37225i		−	2.41873i	−1.76616	+	0.938444i		−	1.00000i	3.31911	−	0.827049i	−2.44077			−1.89170	−	2.10273i	−2.85025			1.37225	−	0.341935i
91.20	0.341935	+	1.37225i		−	2.41873i	−1.76616	+	0.938444i			1.00000i	3.31911	−	0.827049i	2.44077			−1.89170	−	2.10273i	−2.85025			−1.37225	+	0.341935i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
23.b	odd	2	1	inner
92.b	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.e.b	✓	32
4.b	odd	2	1	inner	460.2.e.b	✓	32
23.b	odd	2	1	inner	460.2.e.b	✓	32
92.b	even	2	1	inner	460.2.e.b	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
460.2.e.b	✓	32	1.a	even	1	1	trivial
460.2.e.b	✓	32	4.b	odd	2	1	inner
460.2.e.b	✓	32	23.b	odd	2	1	inner
460.2.e.b	✓	32	92.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{16} + 37T_{3}^{14} + 558T_{3}^{12} + 4419T_{3}^{10} + 19735T_{3}^{8} + 49530T_{3}^{6} + 64840T_{3}^{4} + 34400T_{3}^{2} + 128 \) acting on \(S_{2}^{\mathrm{new}}(460, [\chi])\).