Newform orbit 76.5.j.a

• Label: 76.5.j.a
• Level: $76$
• Weight: $5$
• Character orbit: 76.j
• Analytic conductor: $7.856$
• Analytic rank: $0$
• Dimension: $42$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.85611719437\)
Analytic rank:	\(0\)
Dimension:	\(42\)
Relative dimension:	\(7\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) \)

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		−4.65644	+	12.7935i		0		6.59099	+	37.3793i		0		5.00284	−	8.66518i		0		−79.9406	−	67.0781i		0
13.2		0		−4.13985	+	11.3741i		0		−6.25205	−	35.4571i		0		−25.8702	+	44.8086i		0		−50.1832	−	42.1087i		0
13.3		0		−2.28730	+	6.28431i		0		−2.03045	−	11.5152i		0		38.6373	−	66.9218i		0		27.7888	+	23.3175i		0
13.4		0		−0.180467	+	0.495829i		0		−0.550159	−	3.12011i		0		−25.9990	+	45.0316i		0		61.8363	+	51.8868i		0
13.5		0		2.65366	−	7.29088i		0		0.405227	+	2.29816i		0		23.2726	−	40.3094i		0		15.9346	+	13.3707i		0
13.6		0		3.28951	−	9.03787i		0		7.51461	+	42.6175i		0		−18.8739	+	32.6905i		0		−8.81253	−	7.39459i		0
13.7		0		5.33930	−	14.6696i		0		−7.24101	−	41.0658i		0		−15.7120	+	27.2140i		0		−124.640	−	104.585i		0
21.1		0		−8.26669	+	9.85185i		0		−19.2135	+	6.99315i		0		1.56085	+	2.70347i		0		−14.6554	−	83.1149i		0
21.2		0		−7.77177	+	9.26203i		0		42.9478	−	15.6317i		0		2.15264	+	3.72849i		0		−11.3194	−	64.1954i		0
21.3		0		−0.504186	+	0.600866i		0		−8.75235	+	3.18559i		0		−3.87876	−	6.71820i		0		13.9587	+	79.1635i		0
21.4		0		1.91062	−	2.27699i		0		−16.1447	+	5.87619i		0		23.9804	+	41.5352i		0		12.5313	+	71.0685i		0
21.5		0		2.92113	−	3.48127i		0		20.0929	−	7.31321i		0		−36.0108	−	62.3725i		0		10.4793	+	59.4309i		0
21.6		0		9.11558	−	10.8635i		0		31.4208	−	11.4362i		0		39.9854	+	69.2568i		0		−20.8569	−	118.285i		0
21.7		0		10.9995	−	13.1087i		0		−41.8937	+	15.2481i		0		−26.2709	−	45.5025i		0		−36.7834	−	208.609i		0
29.1		0		−8.26669	−	9.85185i		0		−19.2135	−	6.99315i		0		1.56085	−	2.70347i		0		−14.6554	+	83.1149i		0
29.2		0		−7.77177	−	9.26203i		0		42.9478	+	15.6317i		0		2.15264	−	3.72849i		0		−11.3194	+	64.1954i		0
29.3		0		−0.504186	−	0.600866i		0		−8.75235	−	3.18559i		0		−3.87876	+	6.71820i		0		13.9587	−	79.1635i		0
29.4		0		1.91062	+	2.27699i		0		−16.1447	−	5.87619i		0		23.9804	−	41.5352i		0		12.5313	−	71.0685i		0
29.5		0		2.92113	+	3.48127i		0		20.0929	+	7.31321i		0		−36.0108	+	62.3725i		0		10.4793	−	59.4309i		0
29.6		0		9.11558	+	10.8635i		0		31.4208	+	11.4362i		0		39.9854	−	69.2568i		0		−20.8569	+	118.285i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
19.f	odd	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	76.5.j.a	✓	42
19.f	odd	18	1	inner	76.5.j.a	✓	42

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
76.5.j.a	✓	42	1.a	even	1	1	trivial
76.5.j.a	✓	42	19.f	odd	18	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(76, [\chi])\).