Newform orbit 275.2.n.a

• Label: 275.2.n.a
• Level: $275$
• Weight: $2$
• Character orbit: 275.n
• Analytic conductor: $2.196$
• Analytic rank: $0$
• Dimension: $112$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.n (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.19588605559\)
Analytic rank:	\(0\)
Dimension:	\(112\)
Relative dimension:	\(28\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 112 q - 10 q^{3} - 110 q^{4} - 2 q^{5} - 3 q^{6} + 15 q^{7} + 20 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
104.1		−	2.64121i	−2.63471	+	0.856068i	−4.97601			2.16713	+	0.550932i	2.26106	+	6.95882i	1.78467	+	2.45639i			7.86029i	3.78177	−	2.74762i	1.45513	−	5.72387i
104.2		−	2.59476i	−0.639208	+	0.207691i	−4.73276			−2.04376	−	0.907220i	0.538908	+	1.65859i	0.771926	+	1.06246i			7.09084i	−2.06160	+	1.49784i	−2.35401	+	5.30306i
104.3		−	2.56714i	2.41854	−	0.785832i	−4.59021			1.49077	−	1.66662i	−2.01734	−	6.20874i	−0.316775	−	0.436003i			6.64945i	2.80477	−	2.03778i	−4.27844	−	3.82701i
104.4		−	2.29210i	−0.0176964	+	0.00574990i	−3.25374			2.05295	+	0.886237i	0.0131794	+	0.0405619i	−2.62834	−	3.61760i			2.87370i	−2.42677	+	1.76315i	2.03135	−	4.70556i
104.5		−	2.00725i	−0.871105	+	0.283039i	−2.02906			−1.53768	+	1.62344i	0.568131	+	1.74853i	−1.89953	−	2.61448i			0.0583272i	−1.74834	+	1.27024i	3.25864	+	3.08651i
104.6		−	1.82509i	2.00744	−	0.652255i	−1.33096			−2.02412	−	0.950237i	−1.19043	−	3.66375i	0.713401	+	0.981912i		−	1.22106i	1.17731	−	0.855365i	−1.73427	+	3.69420i
104.7		−	1.80640i	2.21605	−	0.720038i	−1.26307			1.03496	+	1.98213i	−1.30067	−	4.00306i	1.15466	+	1.58925i		−	1.33119i	1.96537	−	1.42793i	3.58052	−	1.86955i
104.8		−	1.47943i	−2.08049	+	0.675992i	−0.188699			−0.383179	−	2.20299i	1.00008	+	3.07793i	0.626474	+	0.862267i		−	2.67968i	1.44443	−	1.04944i	−3.25916	+	0.566885i
104.9		−	1.44761i	−3.12078	+	1.01400i	−0.0955719			−1.50619	+	1.65269i	1.46788	+	4.51767i	0.239084	+	0.329071i		−	2.75687i	6.28402	−	4.56560i	2.39245	+	2.18038i
104.10		−	1.40388i	−0.0605251	+	0.0196658i	0.0291329			1.77727	−	1.35695i	0.0276083	+	0.0849697i	1.88796	+	2.59856i		−	2.84865i	−2.42377	+	1.76098i	−1.90498	−	2.49507i
104.11		−	0.859367i	0.639965	−	0.207937i	1.26149			0.0390615	−	2.23573i	−0.178695	−	0.549965i	−2.42583	−	3.33887i		−	2.80282i	−2.06073	+	1.49721i	−1.92131	−	0.0335682i
104.12		−	0.544914i	−1.46432	+	0.475787i	1.70307			1.86790	+	1.22921i	0.259263	+	0.797929i	0.114947	+	0.158211i		−	2.01785i	−0.509188	+	0.369947i	0.669814	−	1.01784i
104.13		−	0.485157i	1.86732	−	0.606729i	1.76462			−0.612413	+	2.15057i	−0.294359	−	0.905943i	−1.06226	−	1.46207i		−	1.82643i	0.691711	−	0.502558i	1.04336	+	0.297116i
104.14		−	0.0779551i	−0.106980	+	0.0347598i	1.99392			−1.71633	+	1.43325i	0.00270971	+	0.00833962i	2.85921	+	3.93536i		−	0.311347i	−2.41681	+	1.75592i	0.111729	+	0.133797i
104.15			0.246394i	−2.03484	+	0.661160i	1.93929			−1.77063	−	1.36561i	−0.162906	−	0.501373i	1.04003	+	1.43147i			0.970619i	1.27640	−	0.927357i	0.336478	−	0.436273i
104.16			0.404454i	1.20727	−	0.392265i	1.83642			2.13325	−	0.670246i	0.158653	+	0.488285i	0.179397	+	0.246919i			1.55166i	−1.12343	+	0.816217i	0.271084	+	0.862804i
104.17			0.465219i	−2.84068	+	0.922994i	1.78357			1.84120	−	1.26885i	−0.429395	−	1.32154i	−2.23691	−	3.07885i			1.76019i	4.79052	−	3.48052i	0.590295	+	0.856560i
104.18			0.560101i	2.87415	−	0.933868i	1.68629			−2.18166	−	0.490283i	0.523060	+	1.60981i	−0.837741	−	1.15305i			2.06469i	4.96158	−	3.60480i	0.274608	−	1.22195i
104.19			0.993849i	1.06680	−	0.346624i	1.01226			−0.478059	−	2.18437i	0.344492	+	1.06024i	0.832091	+	1.14528i			2.99374i	−1.40914	+	1.02380i	2.17093	−	0.475119i
104.20			1.12189i	−1.75582	+	0.570502i	0.741373			−1.07053	+	1.96315i	−0.640038	−	1.96983i	−1.88017	−	2.58784i			3.07551i	0.330394	−	0.240045i	−2.20243	−	1.20101i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
275.n	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	275.2.n.a	✓	112
11.c	even	5	1		275.2.t.a	yes	112
25.e	even	10	1		275.2.t.a	yes	112
275.n	even	10	1	inner	275.2.n.a	✓	112

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
275.2.n.a	✓	112	1.a	even	1	1	trivial
275.2.n.a	✓	112	275.n	even	10	1	inner
275.2.t.a	yes	112	11.c	even	5	1
275.2.t.a	yes	112	25.e	even	10	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(275, [\chi])\).