Newform orbit 1785.2.g.f

• Label: 1785.2.g.f
• Level: $1785$
• Weight: $2$
• Character orbit: 1785.g
• Analytic conductor: $14.253$
• Analytic rank: $0$
• Dimension: $28$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1785 = 3 \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1785.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.2532967608\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 34 q^{4} - 6 q^{6} - 28 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1429.1		−	2.75921i		−	1.00000i	−5.61324			−2.05164	−	0.889262i	−2.75921				−	1.00000i			9.96967i	−1.00000			−2.45366	+	5.66089i
1429.2		−	2.62546i		−	1.00000i	−4.89305			1.28265	+	1.83162i	−2.62546				−	1.00000i			7.59560i	−1.00000			4.80884	−	3.36754i
1429.3		−	2.50516i			1.00000i	−4.27584			1.66676	+	1.49060i	2.50516					1.00000i			5.70136i	−1.00000			3.73421	−	4.17551i
1429.4		−	2.12979i		−	1.00000i	−2.53601			1.73253	−	1.41363i	−2.12979				−	1.00000i			1.14159i	−1.00000			−3.01073	−	3.68993i
1429.5		−	2.11586i		−	1.00000i	−2.47685			−1.03691	+	1.98112i	−2.11586				−	1.00000i			1.00894i	−1.00000			4.19176	+	2.19394i
1429.6		−	2.05674i			1.00000i	−2.23017			−2.19314	−	0.436033i	2.05674					1.00000i			0.473406i	−1.00000			−0.896806	+	4.51072i
1429.7		−	1.90035i			1.00000i	−1.61135			−0.880375	+	2.05547i	1.90035					1.00000i		−	0.738580i	−1.00000			3.90611	+	1.67302i
1429.8		−	1.69985i		−	1.00000i	−0.889490			1.47723	−	1.67863i	−1.69985				−	1.00000i		−	1.88770i	−1.00000			−2.85341	−	2.51107i
1429.9		−	1.61517i			1.00000i	−0.608780			2.06078	−	0.867874i	1.61517					1.00000i		−	2.24706i	−1.00000			−1.40177	−	3.32851i
1429.10		−	1.01664i			1.00000i	0.966449			−1.82446	−	1.29281i	1.01664					1.00000i		−	3.01580i	−1.00000			−1.31431	+	1.85481i
1429.11		−	0.756905i		−	1.00000i	1.42709			−0.809090	−	2.08456i	−0.756905				−	1.00000i		−	2.59398i	−1.00000			−1.57781	+	0.612405i
1429.12		−	0.395643i			1.00000i	1.84347			1.54954	−	1.61212i	0.395643					1.00000i		−	1.52064i	−1.00000			−0.637825	−	0.613063i
1429.13		−	0.304207i		−	1.00000i	1.90746			0.355135	−	2.20769i	−0.304207				−	1.00000i		−	1.18868i	−1.00000			−0.671593	−	0.108035i
1429.14		−	0.0984277i		−	1.00000i	1.99031			−1.32901	+	1.79826i	−0.0984277				−	1.00000i		−	0.392757i	−1.00000			0.176999	+	0.130811i
1429.15			0.0984277i			1.00000i	1.99031			−1.32901	−	1.79826i	−0.0984277					1.00000i			0.392757i	−1.00000			0.176999	−	0.130811i
1429.16			0.304207i			1.00000i	1.90746			0.355135	+	2.20769i	−0.304207					1.00000i			1.18868i	−1.00000			−0.671593	+	0.108035i
1429.17			0.395643i		−	1.00000i	1.84347			1.54954	+	1.61212i	0.395643				−	1.00000i			1.52064i	−1.00000			−0.637825	+	0.613063i
1429.18			0.756905i			1.00000i	1.42709			−0.809090	+	2.08456i	−0.756905					1.00000i			2.59398i	−1.00000			−1.57781	−	0.612405i
1429.19			1.01664i		−	1.00000i	0.966449			−1.82446	+	1.29281i	1.01664				−	1.00000i			3.01580i	−1.00000			−1.31431	−	1.85481i
1429.20			1.61517i		−	1.00000i	−0.608780			2.06078	+	0.867874i	1.61517				−	1.00000i			2.24706i	−1.00000			−1.40177	+	3.32851i

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	1785.2.g.f	✓	28
5.b	even	2	1	inner	1785.2.g.f	✓	28
5.c	odd	4	1		8925.2.a.cv		14
5.c	odd	4	1		8925.2.a.cw		14

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1785.2.g.f	✓	28	1.a	even	1	1	trivial
1785.2.g.f	✓	28	5.b	even	2	1	inner
8925.2.a.cv		14	5.c	odd	4	1
8925.2.a.cw		14	5.c	odd	4	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^28 + 45*T2^26 + 896*T2^24 + 10400*T2^22 + 78014*T2^20 + 396062*T2^18 + 1384360*T2^16 + 3320812*T2^14 + 5346609*T2^12 + 5523757*T2^10 + 3393832*T2^8 + 1099852*T2^6 + 155872*T2^4 + 8016*T2^2 + 64