Newform orbit 460.2.x.a

• Label: 460.2.x.a
• Level: $460$
• Weight: $2$
• Character orbit: 460.x
• Analytic conductor: $3.673$
• Analytic rank: $0$
• Dimension: $240$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.67311849298\)
Analytic rank:	\(0\)
Dimension:	\(240\)
Relative dimension:	\(12\) over \(\Q(\zeta_{44})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 240 q + 4 q^{3}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1		0		−2.71854	+	1.48444i		0		1.97074	+	1.05650i		0		2.65480	+	3.54640i		0		3.56500	−	5.54725i		0
17.2		0		−1.95329	+	1.06658i		0		0.617840	−	2.14902i		0		0.0518807	+	0.0693045i		0		1.05584	−	1.64292i		0
17.3		0		−1.92230	+	1.04965i		0		0.766931	+	2.10043i		0		−2.30217	−	3.07534i		0		0.971534	−	1.51174i		0
17.4		0		−1.47141	+	0.803448i		0		−1.48903	−	1.66817i		0		0.330540	+	0.441549i		0		−0.102418	+	0.159366i		0
17.5		0		−1.02467	+	0.559510i		0		2.07680	−	0.828788i		0		−2.22248	−	2.96889i		0		−0.885033	+	1.37714i		0
17.6		0		0.302476	−	0.165164i		0		0.209636	+	2.22622i		0		1.78504	+	2.38454i		0		−1.55771	+	2.42384i		0
17.7		0		0.416910	−	0.227650i		0		−2.14737	−	0.623543i		0		−0.887718	−	1.18585i		0		−1.49993	+	2.33394i		0
17.8		0		0.483512	−	0.264018i		0		−0.935821	+	2.03082i		0		−1.13426	−	1.51520i		0		−1.45784	+	2.26845i		0
17.9		0		0.707493	−	0.386321i		0		1.31269	−	1.81021i		0		2.84997	+	3.80711i		0		−1.27062	+	1.97712i		0
17.10		0		1.92117	−	1.04904i		0		−0.336864	−	2.21055i		0		−2.02919	−	2.71068i		0		0.968479	−	1.50698i		0
17.11		0		2.20798	−	1.20565i		0		1.99649	+	1.00699i		0		−0.375619	−	0.501768i		0		1.79966	−	2.80032i		0
17.12		0		2.69738	−	1.47288i		0		−2.20694	+	0.359751i		0		2.19560	+	2.93298i		0		3.48456	−	5.42208i		0
33.1		0		−0.632093	−	2.90569i		0		−1.58894	−	1.57330i		0		0.867718	+	1.58911i		0		−5.31457	+	2.42708i		0
33.2		0		−0.486808	−	2.23782i		0		0.0638162	+	2.23516i		0		1.23306	+	2.25818i		0		−2.04197	+	0.932535i		0
33.3		0		−0.409167	−	1.88091i		0		2.14867	+	0.619038i		0		−1.26125	−	2.30981i		0		−0.641504	+	0.292965i		0
33.4		0		−0.299812	−	1.37822i		0		0.675503	−	2.13159i		0		−0.759843	−	1.39155i		0		0.919306	−	0.419833i		0
33.5		0		−0.0813911	−	0.374149i		0		−2.18808	−	0.460771i		0		0.364123	+	0.666841i		0		2.59553	−	1.18534i		0
33.6		0		0.0980316	+	0.450644i		0		2.20605	−	0.365176i		0		1.83859	+	3.36712i		0		2.53543	−	1.15789i		0
33.7		0		0.132785	+	0.610405i		0		−1.61522	+	1.54631i		0		−2.27438	−	4.16522i		0		2.37393	−	1.08414i		0
33.8		0		0.195370	+	0.898100i		0		−2.15927	−	0.580987i		0		1.50914	+	2.76379i		0		1.96048	−	0.895322i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
23.d	odd	22	1	inner
115.l	even	44	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	460.2.x.a	✓	240
5.c	odd	4	1	inner	460.2.x.a	✓	240
23.d	odd	22	1	inner	460.2.x.a	✓	240
115.l	even	44	1	inner	460.2.x.a	✓	240

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
460.2.x.a	✓	240	1.a	even	1	1	trivial
460.2.x.a	✓	240	5.c	odd	4	1	inner
460.2.x.a	✓	240	23.d	odd	22	1	inner
460.2.x.a	✓	240	115.l	even	44	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(460, [\chi])\).