Newform orbit 555.2.c.c

• Label: 555.2.c.c
• Level: $555$
• Weight: $2$
• Character orbit: 555.c
• Analytic conductor: $4.432$
• Analytic rank: $0$
• Dimension: $26$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.43169731218\)
Analytic rank:	\(0\)
Dimension:	\(26\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 26 q - 32 q^{4} - 2 q^{5} - 26 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
334.1		−	2.77939i		−	1.00000i	−5.72501			−2.22462	+	0.225945i	−2.77939					0.0319162i			10.3533i	−1.00000			0.627991	+	6.18310i
334.2		−	2.55509i			1.00000i	−4.52851			2.13933	−	0.650593i	2.55509				−	2.23683i			6.46057i	−1.00000			−1.66233	−	5.46619i
334.3		−	2.40245i			1.00000i	−3.77179			−1.28557	+	1.82956i	2.40245				−	3.30864i			4.25663i	−1.00000			4.39544	+	3.08853i
334.4		−	2.36117i		−	1.00000i	−3.57513			1.66180	+	1.49613i	−2.36117				−	3.86072i			3.71916i	−1.00000			3.53262	−	3.92381i
334.5		−	2.32415i			1.00000i	−3.40166			−2.03612	−	0.924245i	2.32415					3.18077i			3.25767i	−1.00000			−2.14808	+	4.73224i
334.6		−	1.82554i		−	1.00000i	−1.33258			1.97176	−	1.05459i	−1.82554					4.15424i		−	1.21840i	−1.00000			−1.92520	−	3.59951i
334.7		−	1.59785i		−	1.00000i	−0.553137			−1.43895	+	1.71155i	−1.59785					4.47204i		−	2.31188i	−1.00000			2.73481	+	2.29923i
334.8		−	1.46114i			1.00000i	−0.134925			1.43182	−	1.71753i	1.46114				−	3.04927i		−	2.72513i	−1.00000			−2.50954	−	2.09208i
334.9		−	1.33085i		−	1.00000i	0.228850			1.74423	−	1.39916i	−1.33085				−	3.76351i		−	2.96625i	−1.00000			−1.86207	−	2.32130i
334.10		−	0.919689i			1.00000i	1.15417			−0.388610	−	2.20204i	0.919689				−	0.259618i		−	2.90086i	−1.00000			−2.02519	+	0.357401i
334.11		−	0.550826i			1.00000i	1.69659			−0.808939	+	2.08461i	0.550826					2.51774i		−	2.03618i	−1.00000			1.14826	+	0.445584i
334.12		−	0.214651i		−	1.00000i	1.95393			−2.20564	−	0.367653i	−0.214651					4.41925i		−	0.848712i	−1.00000			−0.0789169	+	0.473441i
334.13		−	0.103900i		−	1.00000i	1.98920			0.439510	−	2.19245i	−0.103900				−	0.609052i		−	0.414478i	−1.00000			−0.227795	−	0.0456650i
334.14			0.103900i			1.00000i	1.98920			0.439510	+	2.19245i	−0.103900					0.609052i			0.414478i	−1.00000			−0.227795	+	0.0456650i
334.15			0.214651i			1.00000i	1.95393			−2.20564	+	0.367653i	−0.214651				−	4.41925i			0.848712i	−1.00000			−0.0789169	−	0.473441i
334.16			0.550826i		−	1.00000i	1.69659			−0.808939	−	2.08461i	0.550826				−	2.51774i			2.03618i	−1.00000			1.14826	−	0.445584i
334.17			0.919689i		−	1.00000i	1.15417			−0.388610	+	2.20204i	0.919689					0.259618i			2.90086i	−1.00000			−2.02519	−	0.357401i
334.18			1.33085i			1.00000i	0.228850			1.74423	+	1.39916i	−1.33085					3.76351i			2.96625i	−1.00000			−1.86207	+	2.32130i
334.19			1.46114i		−	1.00000i	−0.134925			1.43182	+	1.71753i	1.46114					3.04927i			2.72513i	−1.00000			−2.50954	+	2.09208i
334.20			1.59785i			1.00000i	−0.553137			−1.43895	−	1.71155i	−1.59785				−	4.47204i			2.31188i	−1.00000			2.73481	−	2.29923i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	555.2.c.c	✓	26
3.b	odd	2	1		1665.2.c.f		26
5.b	even	2	1	inner	555.2.c.c	✓	26
5.c	odd	4	1		2775.2.a.bg		13
5.c	odd	4	1		2775.2.a.bh		13
15.d	odd	2	1		1665.2.c.f		26
15.e	even	4	1		8325.2.a.cu		13
15.e	even	4	1		8325.2.a.cv		13

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
555.2.c.c	✓	26	1.a	even	1	1	trivial
555.2.c.c	✓	26	5.b	even	2	1	inner
1665.2.c.f		26	3.b	odd	2	1
1665.2.c.f		26	15.d	odd	2	1
2775.2.a.bg		13	5.c	odd	4	1
2775.2.a.bh		13	5.c	odd	4	1
8325.2.a.cu		13	15.e	even	4	1
8325.2.a.cv		13	15.e	even	4	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^26 + 42*T2^24 + 771*T2^22 + 8130*T2^20 + 54435*T2^18 + 241528*T2^16 + 719422*T2^14 + 1425812*T2^12 + 1821683*T2^10 + 1407938*T2^8 + 583595*T2^6 + 101938*T2^4 + 4369*T2^2 + 36