Newform orbit 108.4.i.a

• Label: 108.4.i.a
• Level: $108$
• Weight: $4$
• Character orbit: 108.i
• Analytic conductor: $6.372$
• Analytic rank: $0$
• Dimension: $54$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.37220628062\)
Analytic rank:	\(0\)
Dimension:	\(54\)
Relative dimension:	\(9\) over \(\Q(\zeta_{9})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
13.1		0		−4.52704	+	2.55067i		0		−1.73722	−	1.45770i		0		−5.32680	−	1.93880i		0		13.9881	−	23.0940i		0
13.2		0		−4.40571	−	2.75494i		0		8.18465	+	6.86774i		0		−24.4722	−	8.90714i		0		11.8206	+	24.2749i		0
13.3		0		−4.40211	−	2.76069i		0		−14.9393	−	12.5356i		0		23.5233	+	8.56177i		0		11.7572	+	24.3057i		0
13.4		0		−0.716497	−	5.14652i		0		7.52940	+	6.31792i		0		24.9076	+	9.06562i		0		−25.9733	+	7.37493i		0
13.5		0		−0.173032	+	5.19327i		0		6.54095	+	5.48851i		0		11.9650	+	4.35489i		0		−26.9401	−	1.79720i		0
13.6		0		2.34095	−	4.63896i		0		−5.19451	−	4.35871i		0		−17.8009	−	6.47901i		0		−16.0399	−	21.7191i		0
13.7		0		2.66172	+	4.46265i		0		−12.8040	−	10.7439i		0		−20.8033	−	7.57178i		0		−12.8305	+	23.7566i		0
13.8		0		5.14478	+	0.728858i		0		−5.18194	−	4.34817i		0		16.8240	+	6.12342i		0		25.9375	+	7.49962i		0
13.9		0		5.19029	−	0.246754i		0		15.7004	+	13.1742i		0		−8.81657	−	3.20897i		0		26.8782	−	2.56145i		0
25.1		0		−4.52704	−	2.55067i		0		−1.73722	+	1.45770i		0		−5.32680	+	1.93880i		0		13.9881	+	23.0940i		0
25.2		0		−4.40571	+	2.75494i		0		8.18465	−	6.86774i		0		−24.4722	+	8.90714i		0		11.8206	−	24.2749i		0
25.3		0		−4.40211	+	2.76069i		0		−14.9393	+	12.5356i		0		23.5233	−	8.56177i		0		11.7572	−	24.3057i		0
25.4		0		−0.716497	+	5.14652i		0		7.52940	−	6.31792i		0		24.9076	−	9.06562i		0		−25.9733	−	7.37493i		0
25.5		0		−0.173032	−	5.19327i		0		6.54095	−	5.48851i		0		11.9650	−	4.35489i		0		−26.9401	+	1.79720i		0
25.6		0		2.34095	+	4.63896i		0		−5.19451	+	4.35871i		0		−17.8009	+	6.47901i		0		−16.0399	+	21.7191i		0
25.7		0		2.66172	−	4.46265i		0		−12.8040	+	10.7439i		0		−20.8033	+	7.57178i		0		−12.8305	−	23.7566i		0
25.8		0		5.14478	−	0.728858i		0		−5.18194	+	4.34817i		0		16.8240	−	6.12342i		0		25.9375	−	7.49962i		0
25.9		0		5.19029	+	0.246754i		0		15.7004	−	13.1742i		0		−8.81657	+	3.20897i		0		26.8782	+	2.56145i		0
49.1		0		−5.16735	+	0.546343i		0		5.21695	−	1.89881i		0		1.58868	+	9.00985i		0		26.4030	−	5.64629i		0
49.2		0		−4.14053	+	3.13943i		0		−4.27250	+	1.55506i		0		−4.69568	−	26.6305i		0		7.28791	−	25.9978i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
27.e	even	9	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	108.4.i.a	✓	54
3.b	odd	2	1		324.4.i.a		54
27.e	even	9	1	inner	108.4.i.a	✓	54
27.f	odd	18	1		324.4.i.a		54

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
108.4.i.a	✓	54	1.a	even	1	1	trivial
108.4.i.a	✓	54	27.e	even	9	1	inner
324.4.i.a		54	3.b	odd	2	1
324.4.i.a		54	27.f	odd	18	1

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(108, [\chi])\).