Newform orbit 484.2.i.a

• Label: 484.2.i.a
• Level: $484$
• Weight: $2$
• Character orbit: 484.i
• Analytic conductor: $3.865$
• Analytic rank: $0$
• Dimension: $110$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	484.i (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.86475945783\)
Analytic rank:	\(0\)
Dimension:	\(110\)
Relative dimension:	\(11\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) 110 * q - 2 * q^3 + 2 * q^5 - 2 * q^7 + 112 * q^9 - 10 * q^11 - 29 * q^13 - 18 * q^15 - 6 * q^17 - 8 * q^19 - 2 * q^21 + 4 * q^23 - 17 * q^25 + 4 * q^27 - 28 * q^31 + q^33 + 6 * q^35 - 31 * q^37 + 4 * q^39 + 10 * q^43 - 8 * q^45 + 2 * q^47 - 49 * q^49 + 115 * q^51 + 72 * q^53 + 41 * q^55 + 3 * q^57 - 6 * q^59 + 4 * q^61 - 51 * q^63 - 45 * q^65 - 51 * q^67 + 4 * q^69 + 26 * q^71 - 18 * q^73 + 46 * q^77 - 24 * q^79 + 110 * q^81 - 6 * q^83 - 92 * q^85 - 7 * q^89 - 91 * q^91 - 37 * q^93 - 64 * q^95 - 31 * q^97 - 57 * q^99

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
45.1		0		−3.36389				0		0.594015	+	0.381750i		0		−0.929866	+	0.273033i		0		8.31576				0
45.2		0		−1.97219				0		1.47725	+	0.949373i		0		−4.24017	+	1.24503i		0		0.889514				0
45.3		0		−1.72075				0		−1.94248	−	1.24836i		0		0.240550	−	0.0706320i		0		−0.0390297				0
45.4		0		−1.58623				0		2.56865	+	1.65077i		0		3.39977	−	0.998263i		0		−0.483872				0
45.5		0		−0.848441				0		−0.619315	−	0.398009i		0		0.729996	−	0.214346i		0		−2.28015				0
45.6		0		0.359471				0		−2.27804	−	1.46400i		0		2.56877	−	0.754259i		0		−2.87078				0
45.7		0		0.481063				0		−0.519205	−	0.333673i		0		−3.77609	+	1.10876i		0		−2.76858				0
45.8		0		1.23311				0		2.28756	+	1.47013i		0		1.88432	−	0.553286i		0		−1.47943				0
45.9		0		2.07677				0		−3.50293	−	2.25120i		0		−4.16309	+	1.22239i		0		1.31296				0
45.10		0		2.38838				0		−0.475313	−	0.305465i		0		1.30889	−	0.384324i		0		2.70438				0
45.11		0		2.66807				0		2.64925	+	1.70257i		0		−2.11772	+	0.621820i		0		4.11859				0
89.1		0		−3.27264				0		−0.637588	−	1.39612i		0		2.26780	−	1.45743i		0		7.71020				0
89.2		0		−3.16927				0		1.61924	+	3.54564i		0		−3.41179	+	2.19262i		0		7.04427				0
89.3		0		−1.73399				0		0.756744	+	1.65704i		0		3.78569	−	2.43292i		0		0.00671706				0
89.4		0		−1.70980				0		−1.17644	−	2.57604i		0		−2.29162	+	1.47273i		0		−0.0765820				0
89.5		0		−1.02091				0		−0.267995	−	0.586827i		0		0.493958	−	0.317448i		0		−1.95775				0
89.6		0		−0.0291248				0		0.422800	+	0.925803i		0		−2.63726	+	1.69486i		0		−2.99915				0
89.7		0		0.602184				0		−1.63618	−	3.58272i		0		2.31185	−	1.48574i		0		−2.63737				0
89.8		0		1.38825				0		0.974029	+	2.13282i		0		−1.64826	+	1.05927i		0		−1.07277				0
89.9		0		1.44940				0		1.47314	+	3.22572i		0		3.83701	−	2.46590i		0		−0.899249				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
121.e	even	11	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	484.2.i.a	✓	110
121.e	even	11	1	inner	484.2.i.a	✓	110

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
484.2.i.a	✓	110	1.a	even	1	1	trivial
484.2.i.a	✓	110	121.e	even	11	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(484, [\chi])\).