Newform orbit 555.2.t.a

• Label: 555.2.t.a
• Level: $555$
• Weight: $2$
• Character orbit: 555.t
• Analytic conductor: $4.432$
• Analytic rank: $0$
• Dimension: $76$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.t (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.43169731218\)
Analytic rank:	\(0\)
Dimension:	\(76\)
Relative dimension:	\(38\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 76 q - 4 q^{2} + 76 q^{4} - 8 q^{5} - 12 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
253.1	−2.77825			−0.707107	+	0.707107i	5.71868			−1.30368	−	1.81671i	1.96452	−	1.96452i	0.581510	−	0.581510i	−10.3314				−	1.00000i	3.62194	+	5.04727i
253.2	−2.76175			0.707107	−	0.707107i	5.62727			2.09886	−	0.771235i	−1.95285	+	1.95285i	−3.33142	+	3.33142i	−10.0176				−	1.00000i	−5.79652	+	2.12996i
253.3	−2.46750			0.707107	−	0.707107i	4.08856			−2.09720	+	0.775730i	−1.74479	+	1.74479i	0.637495	−	0.637495i	−5.15353				−	1.00000i	5.17484	−	1.91411i
253.4	−2.35002			0.707107	−	0.707107i	3.52260			−0.308544	−	2.21468i	−1.66172	+	1.66172i	3.20088	−	3.20088i	−3.57815				−	1.00000i	0.725084	+	5.20454i
253.5	−2.33832			−0.707107	+	0.707107i	3.46774			−2.02057	+	0.957766i	1.65344	−	1.65344i	−1.20946	+	1.20946i	−3.43204				−	1.00000i	4.72473	−	2.23956i
253.6	−2.18167			−0.707107	+	0.707107i	2.75970			1.37981	+	1.75958i	1.54268	−	1.54268i	−3.21609	+	3.21609i	−1.65741				−	1.00000i	−3.01028	−	3.83884i
253.7	−2.14734			−0.707107	+	0.707107i	2.61105			−0.0996912	+	2.23384i	1.51840	−	1.51840i	3.59092	−	3.59092i	−1.31213				−	1.00000i	0.214070	−	4.79681i
253.8	−1.96071			0.707107	−	0.707107i	1.84439			0.323120	+	2.21260i	−1.38643	+	1.38643i	−1.21638	+	1.21638i	0.305110				−	1.00000i	−0.633544	−	4.33827i
253.9	−1.63752			−0.707107	+	0.707107i	0.681472			0.356352	−	2.20749i	1.15790	−	1.15790i	−3.15379	+	3.15379i	2.15912				−	1.00000i	−0.583533	+	3.61481i
253.10	−1.63519			0.707107	−	0.707107i	0.673859			2.01119	+	0.977306i	−1.15626	+	1.15626i	0.995027	−	0.995027i	2.16850				−	1.00000i	−3.28868	−	1.59808i
253.11	−1.52490			0.707107	−	0.707107i	0.325322			−2.17799	−	0.506306i	−1.07827	+	1.07827i	−2.71288	+	2.71288i	2.55372				−	1.00000i	3.32122	+	0.772067i
253.12	−1.39635			−0.707107	+	0.707107i	−0.0502077			−1.86470	−	1.23405i	0.987368	−	0.987368i	0.326301	−	0.326301i	2.86281				−	1.00000i	2.60378	+	1.72317i
253.13	−1.36680			−0.707107	+	0.707107i	−0.131863			1.38196	−	1.75789i	0.966472	−	0.966472i	3.07486	−	3.07486i	2.91383				−	1.00000i	−1.88886	+	2.40268i
253.14	−1.04077			0.707107	−	0.707107i	−0.916801			0.544639	−	2.16873i	−0.735934	+	0.735934i	0.963820	−	0.963820i	3.03571				−	1.00000i	−0.566843	+	2.25714i
253.15	−0.939140			−0.707107	+	0.707107i	−1.11802			1.96295	+	1.07091i	0.664072	−	0.664072i	−0.169526	+	0.169526i	2.92825				−	1.00000i	−1.84348	−	1.00573i
253.16	−0.630574			0.707107	−	0.707107i	−1.60238			0.0601426	+	2.23526i	−0.445883	+	0.445883i	2.38542	−	2.38542i	2.27156				−	1.00000i	−0.0379243	−	1.40950i
253.17	−0.580466			0.707107	−	0.707107i	−1.66306			−2.08610	−	0.805095i	−0.410452	+	0.410452i	1.74258	−	1.74258i	2.12628				−	1.00000i	1.21091	+	0.467331i
253.18	−0.238090			−0.707107	+	0.707107i	−1.94331			−2.15440	+	0.598800i	0.168355	−	0.168355i	−1.25056	+	1.25056i	0.938862				−	1.00000i	0.512940	−	0.142568i
253.19	0.0718684			0.707107	−	0.707107i	−1.99483			−1.13521	+	1.92647i	0.0508186	−	0.0508186i	−0.0396475	+	0.0396475i	−0.287102				−	1.00000i	−0.0815856	+	0.138453i
253.20	0.167606			−0.707107	+	0.707107i	−1.97191			−0.187226	−	2.22822i	−0.118515	+	0.118515i	−0.106687	+	0.106687i	−0.665716				−	1.00000i	−0.0313802	−	0.373463i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
185.k	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	555.2.t.a	yes	76
5.c	odd	4	1		555.2.j.a	✓	76
37.d	odd	4	1		555.2.j.a	✓	76
185.k	even	4	1	inner	555.2.t.a	yes	76

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
555.2.j.a	✓	76	5.c	odd	4	1
555.2.j.a	✓	76	37.d	odd	4	1
555.2.t.a	yes	76	1.a	even	1	1	trivial
555.2.t.a	yes	76	185.k	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(555, [\chi])\).