Newform orbit 667.2.c.a

• Label: 667.2.c.a
• Level: $667$
• Weight: $2$
• Character orbit: 667.c
• Analytic conductor: $5.326$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.32602181482\)
Analytic rank:	\(0\)
Dimension:	\(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 20 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 20 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
231.1		−	2.77982i			1.28599i	−5.72740			−2.35144			3.57483			−4.18767					10.3615i	1.34622					6.53657i
231.2		−	2.34828i		−	1.29867i	−3.51441			−0.970368			−3.04964			−2.50083					3.55625i	1.31345					2.27869i
231.3		−	2.11325i		−	0.959214i	−2.46583			−0.304643			−2.02706			3.12570					0.984408i	2.07991					0.643787i
231.4		−	2.08607i			2.80151i	−2.35169			3.58256			5.84415			0.601243					0.733659i	−4.84846				−	7.47347i
231.5		−	2.03160i		−	1.96205i	−2.12738			3.21176			−3.98609			2.40119					0.258793i	−0.849634				−	6.52500i
231.6		−	1.74565i			2.80691i	−1.04728			0.799869			4.89988			−4.45077				−	1.66311i	−4.87877				−	1.39629i
231.7		−	1.40478i			1.16993i	0.0265843			1.02593			1.64349			3.23005				−	2.84691i	1.63127				−	1.44121i
231.8		−	1.15328i		−	0.862739i	0.669940			−1.18254			−0.994981			−1.64078				−	3.07919i	2.25568					1.36380i
231.9		−	0.924253i		−	3.22180i	1.14576			−1.97277			−2.97776			−2.61454				−	2.90748i	−7.38002					1.82334i
231.10		−	0.725687i		−	0.186561i	1.47338			2.03787			−0.135385			−3.50373				−	2.52059i	2.96520				−	1.47886i
231.11		−	0.278327i			1.39492i	1.92253			−3.24586			0.388244			1.41013				−	1.09175i	1.05420					0.903412i
231.12		−	0.0647961i		−	2.77291i	1.99580			2.36963			−0.179674			1.13001				−	0.258912i	−4.68905				−	0.153543i
231.13			0.0647961i			2.77291i	1.99580			2.36963			−0.179674			1.13001					0.258912i	−4.68905					0.153543i
231.14			0.278327i		−	1.39492i	1.92253			−3.24586			0.388244			1.41013					1.09175i	1.05420				−	0.903412i
231.15			0.725687i			0.186561i	1.47338			2.03787			−0.135385			−3.50373					2.52059i	2.96520					1.47886i
231.16			0.924253i			3.22180i	1.14576			−1.97277			−2.97776			−2.61454					2.90748i	−7.38002				−	1.82334i
231.17			1.15328i			0.862739i	0.669940			−1.18254			−0.994981			−1.64078					3.07919i	2.25568				−	1.36380i
231.18			1.40478i		−	1.16993i	0.0265843			1.02593			1.64349			3.23005					2.84691i	1.63127					1.44121i
231.19			1.74565i		−	2.80691i	−1.04728			0.799869			4.89988			−4.45077					1.66311i	−4.87877					1.39629i
231.20			2.03160i			1.96205i	−2.12738			3.21176			−3.98609			2.40119				−	0.258793i	−0.849634					6.52500i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
29.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	667.2.c.a	✓	24
29.b	even	2	1	inner	667.2.c.a	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
667.2.c.a	✓	24	1.a	even	1	1	trivial
667.2.c.a	✓	24	29.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^24 + 34*T2^22 + 497*T2^20 + 4100*T2^18 + 21046*T2^16 + 69858*T2^14 + 150923*T2^12 + 208383*T2^10 + 175682*T2^8 + 82743*T2^6 + 18038*T2^4 + 1027*T2^2 + 4