Newform orbit 109.5.d.a

• Label: 109.5.d.a
• Level: $109$
• Weight: $5$
• Character orbit: 109.d
• Analytic conductor: $11.267$
• Analytic rank: $0$
• Dimension: $70$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 109 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	109.d (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.2673259761\)
Analytic rank:	\(0\)
Dimension:	\(70\)
Relative dimension:	\(35\) over \(\Q(i)\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 70 q + 4 q^{2} - 4 q^{3} - 52 q^{5} - 62 q^{6} - 104 q^{7} + 114 q^{8} + 1806 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
33.1	−5.49903	−	5.49903i	6.35188					44.4786i	5.49366			−34.9291	−	34.9291i	27.7597			156.605	−	156.605i	−40.6537			−30.2098	−	30.2098i
33.2	−5.02935	−	5.02935i	−11.1413					34.5887i	16.7475			56.0337	+	56.0337i	−6.94103			93.4888	−	93.4888i	43.1296			−84.2289	−	84.2289i
33.3	−4.89538	−	4.89538i	−2.24415					31.9295i	−28.8685			10.9860	+	10.9860i	−69.3320			77.9810	−	77.9810i	−75.9638			141.322	+	141.322i
33.4	−4.44610	−	4.44610i	13.9174					23.5355i	−41.0588			−61.8782	−	61.8782i	−18.6536			33.5037	−	33.5037i	112.695			182.552	+	182.552i
33.5	−4.44468	−	4.44468i	12.9025					23.5104i	32.0977			−57.3475	−	57.3475i	−38.4426			33.3813	−	33.3813i	85.4744			−142.664	−	142.664i
33.6	−4.11201	−	4.11201i	−16.6180					17.8172i	−26.6314			68.3332	+	68.3332i	58.3251			7.47227	−	7.47227i	195.157			109.509	+	109.509i
33.7	−4.00925	−	4.00925i	4.95987					16.1482i	−14.3182			−19.8854	−	19.8854i	85.3745			0.594319	−	0.594319i	−56.3997			57.4053	+	57.4053i
33.8	−3.69637	−	3.69637i	−2.60344					11.3262i	34.4391			9.62328	+	9.62328i	28.8593			−17.2759	+	17.2759i	−74.2221			−127.299	−	127.299i
33.9	−3.40629	−	3.40629i	−7.48255					7.20560i	−27.2489			25.4877	+	25.4877i	−22.7197			−29.9563	+	29.9563i	−25.0115			92.8174	+	92.8174i
33.10	−2.52816	−	2.52816i	3.46644				−	3.21677i	21.3871			−8.76373	−	8.76373i	−53.2272			−48.5832	+	48.5832i	−68.9838			−54.0701	−	54.0701i
33.11	−2.42094	−	2.42094i	11.5862				−	4.27810i	−17.5907			−28.0495	−	28.0495i	−29.5149			−49.0921	+	49.0921i	53.2397			42.5861	+	42.5861i
33.12	−2.36177	−	2.36177i	−13.7861				−	4.84413i	30.1719			32.5595	+	32.5595i	−93.7222			−49.2289	+	49.2289i	109.056			−71.2589	−	71.2589i
33.13	−1.70919	−	1.70919i	15.2572				−	10.1574i	21.8887			−26.0773	−	26.0773i	66.4982			−44.7078	+	44.7078i	151.781			−37.4119	−	37.4119i
33.14	−1.66715	−	1.66715i	−3.57581				−	10.4412i	−19.8120			5.96141	+	5.96141i	15.5033			−44.0815	+	44.0815i	−68.2136			33.0295	+	33.0295i
33.15	−1.27656	−	1.27656i	−13.0920				−	12.7408i	17.7897			16.7127	+	16.7127i	59.4198			−36.6894	+	36.6894i	90.3994			−22.7097	−	22.7097i
33.16	−0.0193615	−	0.0193615i	4.24866				−	15.9993i	−0.0782488			−0.0822603	−	0.0822603i	−66.0610			−0.619552	+	0.619552i	−62.9489			0.00151501	+	0.00151501i
33.17	0.0957240	+	0.0957240i	−13.5086				−	15.9817i	−42.4300			−1.29310	−	1.29310i	−57.7930			3.06141	−	3.06141i	101.483			−4.06157	−	4.06157i
33.18	0.286426	+	0.286426i	3.01181				−	15.8359i	39.0779			0.862659	+	0.862659i	37.5978			9.11862	−	9.11862i	−71.9290			11.1929	+	11.1929i
33.19	0.431537	+	0.431537i	2.73058				−	15.6276i	−43.5465			1.17835	+	1.17835i	89.4933			13.6485	−	13.6485i	−73.5439			−18.7920	−	18.7920i
33.20	0.466959	+	0.466959i	13.7512				−	15.5639i	−22.0742			6.42127	+	6.42127i	−2.19206			14.7390	−	14.7390i	108.097			−10.3078	−	10.3078i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
109.d	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	109.5.d.a	✓	70
109.d	odd	4	1	inner	109.5.d.a	✓	70

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
109.5.d.a	✓	70	1.a	even	1	1	trivial
109.5.d.a	✓	70	109.d	odd	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(109, [\chi])\).