Newform orbit 451.3.c.a

• Label: 451.3.c.a
• Level: $451$
• Weight: $3$
• Character orbit: 451.c
• Analytic conductor: $12.289$
• Analytic rank: $0$
• Dimension: $80$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 451 = 11 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	451.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(12.2888599226\)
Analytic rank:	\(0\)
Dimension:	\(80\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 80 q - 2 q^{3} - 172 q^{4} - 2 q^{5} + 222 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
329.1		−	3.86740i	0.284787			−10.9567			6.80301				−	1.10139i		−	10.0258i			26.9045i	−8.91890				−	26.3099i
329.2		−	3.81545i	−3.47310			−10.5577			5.73162					13.2514i			12.0719i			25.0204i	3.06243				−	21.8687i
329.3		−	3.80941i	−5.74469			−10.5116			−1.41557					21.8839i		−	8.06994i			24.8055i	24.0014					5.39250i
329.4		−	3.70630i	2.61786			−9.73665			−2.57165				−	9.70256i			0.554988i			21.2617i	−2.14682					9.53131i
329.5		−	3.66482i	1.47422			−9.43091			−0.435870				−	5.40275i			4.22860i			19.9033i	−6.82668					1.59738i
329.6		−	3.63868i	5.44784			−9.23999			5.23975				−	19.8230i			9.04380i			19.0667i	20.6790				−	19.0658i
329.7		−	3.61216i	−2.21615			−9.04772			−9.63040					8.00510i			3.52489i			18.2332i	−4.08868					34.7866i
329.8		−	3.56233i	5.73019			−8.69019			−5.12597				−	20.4128i		−	12.4737i			16.7080i	23.8350					18.2604i
329.9		−	3.42301i	−2.64594			−7.71702			−3.85062					9.05707i			3.30830i			12.7234i	−1.99903					13.1807i
329.10		−	3.12406i	−2.30747			−5.75977			−3.34617					7.20868i		−	10.0654i			5.49762i	−3.67558					10.4537i
329.11		−	3.04571i	−2.65498			−5.27637			6.96423					8.08631i			1.15638i			3.88747i	−1.95109				−	21.2110i
329.12		−	3.03480i	1.31627			−5.21001			4.08394				−	3.99462i		−	5.24882i			3.67213i	−7.26743				−	12.3940i
329.13		−	2.97307i	−4.58191			−4.83912			5.03045					13.6223i		−	5.37946i			2.49475i	11.9939				−	14.9559i
329.14		−	2.91383i	4.14078			−4.49040			8.35982				−	12.0655i		−	7.14160i			1.42895i	8.14602				−	24.3591i
329.15		−	2.90383i	3.85533			−4.43223			−3.50048				−	11.1952i			2.81847i			1.25512i	5.86360					10.1648i
329.16		−	2.81588i	1.19559			−3.92920			−7.58022				−	3.36666i		−	11.5969i		−	0.199371i	−7.57055					21.3450i
329.17		−	2.71971i	−0.644618			−3.39681			1.01016					1.75317i			4.90992i		−	1.64051i	−8.58447				−	2.74734i
329.18		−	2.66358i	3.90487			−3.09467			−8.87351				−	10.4010i			12.7972i		−	2.41141i	6.24803					23.6353i
329.19		−	2.33111i	1.03569			−1.43409			8.82146				−	2.41432i			9.92341i		−	5.98143i	−7.92734				−	20.5638i
329.20		−	2.29037i	−4.44533			−1.24580			1.21889					10.1815i		−	1.03773i		−	6.30814i	10.7610				−	2.79172i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	451.3.c.a	✓	80
11.b	odd	2	1	inner	451.3.c.a	✓	80

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
451.3.c.a	✓	80	1.a	even	1	1	trivial
451.3.c.a	✓	80	11.b	odd	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(451, [\chi])\).