Newform orbit 725.2.j.c

• Label: 725.2.j.c
• Level: $725$
• Weight: $2$
• Character orbit: 725.j
• Analytic conductor: $5.789$
• Analytic rank: $0$
• Dimension: $26$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.78915414654\)
Analytic rank:	\(0\)
Dimension:	\(26\)
Relative dimension:	\(13\) over \(\Q(i)\)
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 26 q + 6 q^{2} + 22 q^{4} + 4 q^{7} + 18 q^{8} - 10 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
307.1	−2.26693				−	2.65401i	3.13899				0				6.01647i	2.59753	+	2.59753i	−2.58201			−4.04378				0
307.2	−2.23019					1.25170i	2.97373				0			−	2.79153i	−0.483409	−	0.483409i	−2.17160			1.43324				0
307.3	−1.41066					2.58872i	−0.0100302				0			−	3.65181i	0.510628	+	0.510628i	2.83547			−3.70148				0
307.4	−1.26373				−	0.913274i	−0.402981				0				1.15413i	−2.03055	−	2.03055i	3.03672			2.16593				0
307.5	−0.895351				−	2.11245i	−1.19835				0				1.89138i	−1.38465	−	1.38465i	2.86364			−1.46244				0
307.6	−0.222351					1.02589i	−1.95056				0			−	0.228107i	2.35964	+	2.35964i	0.878412			1.94756				0
307.7	0.342532				−	2.64611i	−1.88267				0			−	0.906377i	1.55474	+	1.55474i	−1.32994			−4.00189				0
307.8	0.839004					0.711801i	−1.29607				0				0.597203i	−1.13987	−	1.13987i	−2.76542			2.49334				0
307.9	1.36192				−	0.228160i	−0.145179				0			−	0.310736i	−3.45046	−	3.45046i	−2.92156			2.94794				0
307.10	1.77873				−	1.38965i	1.16389				0			−	2.47181i	3.41296	+	3.41296i	−1.48721			1.06888				0
307.11	1.82099					2.59340i	1.31599				0				4.72256i	0.820621	+	0.820621i	−1.24557			−3.72575				0
307.12	2.41122				−	1.85973i	3.81399				0			−	4.48422i	0.291676	+	0.291676i	4.37394			−0.458586				0
307.13	2.73482					1.63186i	5.47925				0				4.46285i	−1.05887	−	1.05887i	9.51511			0.337028				0
418.1	−2.26693					2.65401i	3.13899				0			−	6.01647i	2.59753	−	2.59753i	−2.58201			−4.04378				0
418.2	−2.23019				−	1.25170i	2.97373				0				2.79153i	−0.483409	+	0.483409i	−2.17160			1.43324				0
418.3	−1.41066				−	2.58872i	−0.0100302				0				3.65181i	0.510628	−	0.510628i	2.83547			−3.70148				0
418.4	−1.26373					0.913274i	−0.402981				0			−	1.15413i	−2.03055	+	2.03055i	3.03672			2.16593				0
418.5	−0.895351					2.11245i	−1.19835				0			−	1.89138i	−1.38465	+	1.38465i	2.86364			−1.46244				0
418.6	−0.222351				−	1.02589i	−1.95056				0				0.228107i	2.35964	−	2.35964i	0.878412			1.94756				0
418.7	0.342532					2.64611i	−1.88267				0				0.906377i	1.55474	−	1.55474i	−1.32994			−4.00189				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
145.j	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	725.2.j.c		26
5.b	even	2	1		145.2.j.a	yes	26
5.c	odd	4	1		145.2.e.a	✓	26
5.c	odd	4	1		725.2.e.c		26
29.c	odd	4	1		725.2.e.c		26
145.e	even	4	1		145.2.j.a	yes	26
145.f	odd	4	1		145.2.e.a	✓	26
145.j	even	4	1	inner	725.2.j.c		26

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
145.2.e.a	✓	26	5.c	odd	4	1
145.2.e.a	✓	26	145.f	odd	4	1
145.2.j.a	yes	26	5.b	even	2	1
145.2.j.a	yes	26	145.e	even	4	1
725.2.e.c		26	5.c	odd	4	1
725.2.e.c		26	29.c	odd	4	1
725.2.j.c		26	1.a	even	1	1	trivial
725.2.j.c		26	145.j	even	4	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^13 - 3*T2^12 - 14*T2^11 + 44*T2^10 + 69*T2^9 - 235*T2^8 - 142*T2^7 + 562*T2^6 + 113*T2^5 - 607*T2^4 - 8*T2^3 + 246*T2^2 - 19*T2 - 15