Newform orbit 196.2.i.a

• Label: 196.2.i.a
• Level: $196$
• Weight: $2$
• Character orbit: 196.i
• Analytic conductor: $1.565$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.i (of order \(7\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.56506787962\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(4\) over \(\Q(\zeta_{7})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
29.1		0		−0.330037	−	1.44599i		0		−0.641803	−	2.81192i		0		−2.31878	+	1.27408i		0		0.720957	−	0.347195i		0
29.2		0		−0.256242	−	1.12267i		0		0.815122	+	3.57128i		0		0.561713	+	2.58544i		0		1.50818	−	0.726301i		0
29.3		0		0.00303208	+	0.0132844i		0		−0.143963	−	0.630741i		0		0.747328	−	2.53801i		0		2.70274	−	1.30157i		0
29.4		0		0.583247	+	2.55537i		0		−0.196919	−	0.862757i		0		1.68818	+	2.03716i		0		−3.48683	+	1.67917i		0
57.1		0		−2.78599	+	1.34166i		0		−1.35994	+	0.654911i		0		0.781172	−	2.52780i		0		4.09120	−	5.13021i		0
57.2		0		−0.263834	+	0.127056i		0		−3.10119	+	1.49345i		0		−2.58653	+	0.556663i		0		−1.81700	+	2.27845i		0
57.3		0		0.851544	−	0.410082i		0		2.34535	−	1.12946i		0		−0.840460	−	2.50871i		0		−1.31351	+	1.64709i		0
57.4		0		2.19828	−	1.05863i		0		−0.0871332	+	0.0419612i		0		1.12136	+	2.39636i		0		1.84125	−	2.30885i		0
85.1		0		−1.42029	−	1.78099i		0		2.25675	+	2.82987i		0		2.55379	−	0.691491i		0		−0.487128	+	2.13425i		0
85.2		0		−0.753864	−	0.945315i		0		−0.687971	−	0.862688i		0		−2.39160	−	1.13147i		0		0.342253	−	1.49951i		0
85.3		0		0.815653	+	1.02280i		0		0.373508	+	0.468364i		0		1.78408	−	1.95373i		0		0.286740	−	1.25629i		0
85.4		0		1.35850	+	1.70351i		0		0.428183	+	0.536924i		0		−1.10026	+	2.40612i		0		−0.388845	+	1.70364i		0
113.1		0		−1.42029	+	1.78099i		0		2.25675	−	2.82987i		0		2.55379	+	0.691491i		0		−0.487128	−	2.13425i		0
113.2		0		−0.753864	+	0.945315i		0		−0.687971	+	0.862688i		0		−2.39160	+	1.13147i		0		0.342253	+	1.49951i		0
113.3		0		0.815653	−	1.02280i		0		0.373508	−	0.468364i		0		1.78408	+	1.95373i		0		0.286740	+	1.25629i		0
113.4		0		1.35850	−	1.70351i		0		0.428183	−	0.536924i		0		−1.10026	−	2.40612i		0		−0.388845	−	1.70364i		0
141.1		0		−2.78599	−	1.34166i		0		−1.35994	−	0.654911i		0		0.781172	+	2.52780i		0		4.09120	+	5.13021i		0
141.2		0		−0.263834	−	0.127056i		0		−3.10119	−	1.49345i		0		−2.58653	−	0.556663i		0		−1.81700	−	2.27845i		0
141.3		0		0.851544	+	0.410082i		0		2.34535	+	1.12946i		0		−0.840460	+	2.50871i		0		−1.31351	−	1.64709i		0
141.4		0		2.19828	+	1.05863i		0		−0.0871332	−	0.0419612i		0		1.12136	−	2.39636i		0		1.84125	+	2.30885i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
49.e	even	7	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	196.2.i.a	✓	24
4.b	odd	2	1		784.2.u.e		24
49.e	even	7	1	inner	196.2.i.a	✓	24
49.e	even	7	1		9604.2.a.c		12
49.f	odd	14	1		9604.2.a.a		12
196.k	odd	14	1		784.2.u.e		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
196.2.i.a	✓	24	1.a	even	1	1	trivial
196.2.i.a	✓	24	49.e	even	7	1	inner
784.2.u.e		24	4.b	odd	2	1
784.2.u.e		24	196.k	odd	14	1
9604.2.a.a		12	49.f	odd	14	1
9604.2.a.c		12	49.e	even	7	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(196, [\chi])\).