Newform orbit 128.14.e.a

• Label: 128.14.e.a
• Level: $128$
• Weight: $14$
• Character orbit: 128.e
• Analytic conductor: $137.256$
• Analytic rank: $0$
• Dimension: $50$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	128.e (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(137.255589058\)
Analytic rank:	\(0\)
Dimension:	\(50\)
Relative dimension:	\(25\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 50 q - 2 q^{3} + 2 q^{5}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
33.1		0		−1639.97	−	1639.97i		0		−9558.16	+	9558.16i		0			−	133901.i		0				3.78468e6i		0
33.2		0		−1618.47	−	1618.47i		0		23191.8	−	23191.8i		0				280152.i		0				3.64459e6i		0
33.3		0		−1316.54	−	1316.54i		0		43811.8	−	43811.8i		0			−	156812.i		0				1.87225e6i		0
33.4		0		−1272.65	−	1272.65i		0		−36491.5	+	36491.5i		0			−	68080.2i		0				1.64493e6i		0
33.5		0		−1056.56	−	1056.56i		0		−11923.3	+	11923.3i		0				170872.i		0				638332.i		0
33.6		0		−1009.54	−	1009.54i		0		19923.8	−	19923.8i		0			−	484985.i		0				444038.i		0
33.7		0		−924.404	−	924.404i		0		−42023.8	+	42023.8i		0			−	291398.i		0				114722.i		0
33.8		0		−787.355	−	787.355i		0		−13376.5	+	13376.5i		0				547213.i		0			−	354466.i		0
33.9		0		−660.650	−	660.650i		0		6982.48	−	6982.48i		0				294350.i		0			−	721406.i		0
33.10		0		−336.873	−	336.873i		0		6822.00	−	6822.00i		0			−	509047.i		0			−	1.36736e6i		0
33.11		0		−230.668	−	230.668i		0		3615.07	−	3615.07i		0			−	262248.i		0			−	1.48791e6i		0
33.12		0		−217.732	−	217.732i		0		36424.0	−	36424.0i		0				397405.i		0			−	1.49951e6i		0
33.13		0		−26.4760	−	26.4760i		0		38066.2	−	38066.2i		0				23704.0i		0			−	1.59292e6i		0
33.14		0		242.259	+	242.259i		0		−42421.3	+	42421.3i		0				421955.i		0			−	1.47694e6i		0
33.15		0		293.446	+	293.446i		0		−22716.6	+	22716.6i		0			−	343566.i		0			−	1.42210e6i		0
33.16		0		375.766	+	375.766i		0		11477.0	−	11477.0i		0				9991.15i		0			−	1.31192e6i		0
33.17		0		381.223	+	381.223i		0		−29472.6	+	29472.6i		0			−	167372.i		0			−	1.30366e6i		0
33.18		0		805.865	+	805.865i		0		−18822.0	+	18822.0i		0			−	17326.7i		0			−	295487.i		0
33.19		0		913.885	+	913.885i		0		−15715.7	+	15715.7i		0				356100.i		0				76047.5i		0
33.20		0		983.557	+	983.557i		0		35371.2	−	35371.2i		0				334186.i		0				340445.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	128.14.e.a		50
4.b	odd	2	1		128.14.e.b		50
8.b	even	2	1		64.14.e.a		50
8.d	odd	2	1		16.14.e.a	✓	50
16.e	even	4	1		64.14.e.a		50
16.e	even	4	1	inner	128.14.e.a		50
16.f	odd	4	1		16.14.e.a	✓	50
16.f	odd	4	1		128.14.e.b		50

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
16.14.e.a	✓	50	8.d	odd	2	1
16.14.e.a	✓	50	16.f	odd	4	1
64.14.e.a		50	8.b	even	2	1
64.14.e.a		50	16.e	even	4	1
128.14.e.a		50	1.a	even	1	1	trivial
128.14.e.a		50	16.e	even	4	1	inner
128.14.e.b		50	4.b	odd	2	1
128.14.e.b		50	16.f	odd	4	1