Newform orbit 925.2.o.c

• Label: 925.2.o.c
• Level: $925$
• Weight: $2$
• Character orbit: 925.o
• Analytic conductor: $7.386$
• Analytic rank: $0$
• Dimension: $28$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.38616218697\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 16 q^{4} + 8 q^{6} + 10 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
174.1	−2.37929	+	1.37369i	−0.830570	−	0.479530i	2.77403	−	4.80475i		0		2.63489			−0.542327	−	0.313113i			9.74781i	−1.04010	−	1.80151i		0
174.2	−2.14882	+	1.24062i	−1.90884	−	1.10207i	2.07829	−	3.59971i		0		5.46902			−3.31440	−	1.91357i			5.35102i	0.929125	+	1.60929i		0
174.3	−1.63699	+	0.945119i	2.42036	+	1.39740i	0.786500	−	1.36226i		0		−5.28283			−2.51695	−	1.45316i		−	0.807130i	2.40544	+	4.16634i		0
174.4	−1.37708	+	0.795055i	1.34979	+	0.779300i	0.264225	−	0.457651i		0		−2.47835			−1.38761	−	0.801138i		−	2.33993i	−0.285383	−	0.494298i		0
174.5	−1.22029	+	0.704536i	−0.133660	−	0.0771688i	−0.00725754	+	0.0125704i		0		0.217473			2.08952	+	1.20638i		−	2.83860i	−1.48809	−	2.57745i		0
174.6	−0.290053	+	0.167462i	−2.06880	−	1.19442i	−0.943913	+	1.63491i		0		0.800081			−3.83679	−	2.21517i		−	1.30213i	1.35329	+	2.34397i		0
174.7	−0.268684	+	0.155125i	−1.78566	−	1.03095i	−0.951873	+	1.64869i		0		0.639704			−1.83659	−	1.06035i		−	1.21113i	0.625722	+	1.08378i		0
174.8	0.268684	−	0.155125i	1.78566	+	1.03095i	−0.951873	+	1.64869i		0		0.639704			1.83659	+	1.06035i			1.21113i	0.625722	+	1.08378i		0
174.9	0.290053	−	0.167462i	2.06880	+	1.19442i	−0.943913	+	1.63491i		0		0.800081			3.83679	+	2.21517i			1.30213i	1.35329	+	2.34397i		0
174.10	1.22029	−	0.704536i	0.133660	+	0.0771688i	−0.00725754	+	0.0125704i		0		0.217473			−2.08952	−	1.20638i			2.83860i	−1.48809	−	2.57745i		0
174.11	1.37708	−	0.795055i	−1.34979	−	0.779300i	0.264225	−	0.457651i		0		−2.47835			1.38761	+	0.801138i			2.33993i	−0.285383	−	0.494298i		0
174.12	1.63699	−	0.945119i	−2.42036	−	1.39740i	0.786500	−	1.36226i		0		−5.28283			2.51695	+	1.45316i			0.807130i	2.40544	+	4.16634i		0
174.13	2.14882	−	1.24062i	1.90884	+	1.10207i	2.07829	−	3.59971i		0		5.46902			3.31440	+	1.91357i		−	5.35102i	0.929125	+	1.60929i		0
174.14	2.37929	−	1.37369i	0.830570	+	0.479530i	2.77403	−	4.80475i		0		2.63489			0.542327	+	0.313113i		−	9.74781i	−1.04010	−	1.80151i		0
824.1	−2.37929	−	1.37369i	−0.830570	+	0.479530i	2.77403	+	4.80475i		0		2.63489			−0.542327	+	0.313113i		−	9.74781i	−1.04010	+	1.80151i		0
824.2	−2.14882	−	1.24062i	−1.90884	+	1.10207i	2.07829	+	3.59971i		0		5.46902			−3.31440	+	1.91357i		−	5.35102i	0.929125	−	1.60929i		0
824.3	−1.63699	−	0.945119i	2.42036	−	1.39740i	0.786500	+	1.36226i		0		−5.28283			−2.51695	+	1.45316i			0.807130i	2.40544	−	4.16634i		0
824.4	−1.37708	−	0.795055i	1.34979	−	0.779300i	0.264225	+	0.457651i		0		−2.47835			−1.38761	+	0.801138i			2.33993i	−0.285383	+	0.494298i		0
824.5	−1.22029	−	0.704536i	−0.133660	+	0.0771688i	−0.00725754	−	0.0125704i		0		0.217473			2.08952	−	1.20638i			2.83860i	−1.48809	+	2.57745i		0
824.6	−0.290053	−	0.167462i	−2.06880	+	1.19442i	−0.943913	−	1.63491i		0		0.800081			−3.83679	+	2.21517i			1.30213i	1.35329	−	2.34397i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
37.c	even	3	1	inner
185.n	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	925.2.o.c		28
5.b	even	2	1	inner	925.2.o.c		28
5.c	odd	4	1		185.2.e.b	✓	14
5.c	odd	4	1		925.2.e.b		14
37.c	even	3	1	inner	925.2.o.c		28
185.n	even	6	1	inner	925.2.o.c		28
185.r	odd	12	1		6845.2.a.m		7
185.s	odd	12	1		185.2.e.b	✓	14
185.s	odd	12	1		925.2.e.b		14
185.s	odd	12	1		6845.2.a.j		7

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
185.2.e.b	✓	14	5.c	odd	4	1
185.2.e.b	✓	14	185.s	odd	12	1
925.2.e.b		14	5.c	odd	4	1
925.2.e.b		14	185.s	odd	12	1
925.2.o.c		28	1.a	even	1	1	trivial
925.2.o.c		28	5.b	even	2	1	inner
925.2.o.c		28	37.c	even	3	1	inner
925.2.o.c		28	185.n	even	6	1	inner
6845.2.a.j		7	185.s	odd	12	1
6845.2.a.m		7	185.r	odd	12	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^28 - 22*T2^26 + 301*T2^24 - 2584*T2^22 + 16254*T2^20 - 72628*T2^18 + 244822*T2^16 - 592554*T2^14 + 1060367*T2^12 - 1238174*T2^10 + 940169*T2^8 - 180425*T2^6 + 25096*T2^4 - 1683*T2^2 + 81