Embedded newform 105.4.g.b.104.25

• Label: 105.4.g.b.104.25
• Level: $105$
• Weight: $4$
• Character: 105.104
• Analytic conductor: $6.195$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.19520055060\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			104.25
Character	\(\chi\)	\(=\)	105.104
Dual form			105.4.g.b.104.26

$q$-expansion

\(f(q)\)	\(=\)	\(q+2.24438 q^{2} +(-1.06702 - 5.08542i) q^{3} -2.96275 q^{4} +(-8.51335 - 7.24727i) q^{5} +(-2.39479 - 11.4136i) q^{6} +(12.2768 + 13.8665i) q^{7} -24.6046 q^{8} +(-24.7230 + 10.8524i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 184 q^{4} + 4 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\)	\(22\)	\(31\)	\(71\)
\(\chi(n)\)	\(-1\)	\(-1\)	\(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

(See \(a_n\) instead)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	2.24438			0.793509			0.396754	−	0.917925i	\(-0.370136\pi\)
							0.396754	+	0.917925i	\(0.370136\pi\)
\(3\)	−1.06702	−	5.08542i	−0.205347	−	0.978689i
							\(5\)	−8.51335	−	7.24727i	−0.761457	−	0.648215i
\(7\)	12.2768	+	13.8665i	0.662886	+	0.748721i
							\(11\)		−	25.7488i		−	0.705779i	−0.935665	−	0.352889i	\(-0.885199\pi\)
0.935665	−	0.352889i	\(-0.114801\pi\)
\(13\)	−68.2910			−1.45696			−0.728481	−	0.685066i	\(-0.759773\pi\)
							−0.728481	+	0.685066i	\(0.759773\pi\)
\(17\)		−	30.6502i		−	0.437281i	−0.975806	−	0.218640i	\(-0.929838\pi\)
							0.975806	−	0.218640i	\(-0.0701621\pi\)
\(19\)		−	109.632i		−	1.32375i	−0.749615	−	0.661874i	\(-0.769761\pi\)
							0.749615	−	0.661874i	\(-0.230239\pi\)
\(23\)	152.265			1.38041			0.690206	−	0.723613i	\(-0.257520\pi\)
							0.690206	+	0.723613i	\(0.257520\pi\)
\(29\)		−	191.763i		−	1.22791i	−0.789340	−	0.613956i	\(-0.789577\pi\)
							0.789340	−	0.613956i	\(-0.210423\pi\)
\(31\)		−	16.4683i		−	0.0954130i	−0.998861	−	0.0477065i	\(-0.984809\pi\)
							0.998861	−	0.0477065i	\(-0.0151912\pi\)
\(37\)		−	81.9337i		−	0.364049i	−0.983294	−	0.182025i	\(-0.941735\pi\)
							0.983294	−	0.182025i	\(-0.0582651\pi\)
\(41\)	−372.656			−1.41949			−0.709745	−	0.704459i	\(-0.751190\pi\)
							−0.709745	+	0.704459i	\(0.751190\pi\)
\(43\)		−	192.593i		−	0.683028i	−0.939877	−	0.341514i	\(-0.889060\pi\)
							0.939877	−	0.341514i	\(-0.110940\pi\)
\(47\)			0.366739i			0.00113818i	1.00000		0.000569089i	\(0.000181147\pi\)
							−1.00000		0.000569089i	\(0.999819\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.g.b.104.25	yes	40
3.2	odd	2	inner	105.4.g.b.104.14	yes	40
5.4	even	2	inner	105.4.g.b.104.16	yes	40
7.6	odd	2	inner	105.4.g.b.104.28	yes	40
15.14	odd	2	inner	105.4.g.b.104.27	yes	40
21.20	even	2	inner	105.4.g.b.104.15	yes	40
35.34	odd	2	inner	105.4.g.b.104.13	✓	40
105.104	even	2	inner	105.4.g.b.104.26	yes	40

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.g.b.104.13	✓	40	35.34	odd	2	inner
105.4.g.b.104.14	yes	40	3.2	odd	2	inner
105.4.g.b.104.15	yes	40	21.20	even	2	inner
105.4.g.b.104.16	yes	40	5.4	even	2	inner
105.4.g.b.104.25	yes	40	1.1	even	1	trivial
105.4.g.b.104.26	yes	40	105.104	even	2	inner
105.4.g.b.104.27	yes	40	15.14	odd	2	inner
105.4.g.b.104.28	yes	40	7.6	odd	2	inner