Newform orbit 64.12.e.a

• Label: 64.12.e.a
• Level: $64$
• Weight: $12$
• Character orbit: 64.e
• Analytic conductor: $49.174$
• Analytic rank: $0$
• Dimension: $42$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	64.e (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(49.1739635558\)
Analytic rank:	\(0\)
Dimension:	\(42\)
Relative dimension:	\(21\) over \(\Q(i)\)
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 42 q + 2 q^{3} - 2 q^{5}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1		0		−585.540	−	585.540i		0		−6859.07	+	6859.07i		0				19914.8i		0				508568.i		0
17.2		0		−457.250	−	457.250i		0		5575.43	−	5575.43i		0				55452.7i		0				241008.i		0
17.3		0		−442.035	−	442.035i		0		2497.66	−	2497.66i		0			−	39392.3i		0				213643.i		0
17.4		0		−396.720	−	396.720i		0		7616.23	−	7616.23i		0			−	16490.4i		0				137626.i		0
17.5		0		−367.824	−	367.824i		0		−502.344	+	502.344i		0			−	33063.2i		0				93442.1i		0
17.6		0		−255.917	−	255.917i		0		−4214.49	+	4214.49i		0				80345.3i		0			−	46160.2i		0
17.7		0		−221.481	−	221.481i		0		−7918.20	+	7918.20i		0			−	76836.1i		0			−	79039.1i		0
17.8		0		−219.312	−	219.312i		0		−4575.66	+	4575.66i		0				2778.29i		0			−	80951.6i		0
17.9		0		−137.041	−	137.041i		0		3899.66	−	3899.66i		0				37938.5i		0			−	139586.i		0
17.10		0		−13.6026	−	13.6026i		0		−3501.81	+	3501.81i		0				37649.1i		0			−	176777.i		0
17.11		0		4.32776	+	4.32776i		0		2233.99	−	2233.99i		0			−	71414.8i		0			−	177110.i		0
17.12		0		56.4628	+	56.4628i		0		6260.45	−	6260.45i		0			−	32944.0i		0			−	170771.i		0
17.13		0		145.072	+	145.072i		0		−4652.81	+	4652.81i		0				43253.0i		0			−	135056.i		0
17.14		0		179.701	+	179.701i		0		2961.29	−	2961.29i		0			−	5179.04i		0			−	112562.i		0
17.15		0		199.508	+	199.508i		0		8937.54	−	8937.54i		0				55653.3i		0			−	97540.0i		0
17.16		0		291.167	+	291.167i		0		−9753.88	+	9753.88i		0			−	16447.0i		0			−	7590.38i		0
17.17		0		296.568	+	296.568i		0		−2867.98	+	2867.98i		0			−	8380.90i		0			−	1242.24i		0
17.18		0		435.014	+	435.014i		0		−1517.34	+	1517.34i		0			−	59722.7i		0				201326.i		0
17.19		0		475.976	+	475.976i		0		2805.14	−	2805.14i		0				76033.6i		0				275960.i		0
17.20		0		491.248	+	491.248i		0		6777.57	−	6777.57i		0			−	47511.7i		0				305503.i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
16.e	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	64.12.e.a		42
4.b	odd	2	1		16.12.e.a	✓	42
8.b	even	2	1		128.12.e.a		42
8.d	odd	2	1		128.12.e.b		42
16.e	even	4	1	inner	64.12.e.a		42
16.e	even	4	1		128.12.e.a		42
16.f	odd	4	1		16.12.e.a	✓	42
16.f	odd	4	1		128.12.e.b		42

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
16.12.e.a	✓	42	4.b	odd	2	1
16.12.e.a	✓	42	16.f	odd	4	1
64.12.e.a		42	1.a	even	1	1	trivial
64.12.e.a		42	16.e	even	4	1	inner
128.12.e.a		42	8.b	even	2	1
128.12.e.a		42	16.e	even	4	1
128.12.e.b		42	8.d	odd	2	1
128.12.e.b		42	16.f	odd	4	1

Hecke kernels

This newform subspace is the entire newspace \(S_{12}^{\mathrm{new}}(64, [\chi])\).