Newform orbit 35.5.l.a

• Label: 35.5.l.a
• Level: $35$
• Weight: $5$
• Character orbit: 35.l
• Analytic conductor: $3.618$
• Analytic rank: $0$
• Dimension: $56$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.l (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.61794870793\)
Analytic rank:	\(0\)
Dimension:	\(56\)
Relative dimension:	\(14\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 56 q - 2 q^{2} - 2 q^{3} + 16 q^{5} - 144 q^{6} + 46 q^{7} + 108 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−6.91084	+	1.85175i	0.723742	+	0.193926i	30.4743	−	17.5943i	20.7271	+	13.9781i	−5.36076			−44.7877	+	19.8761i	−97.0771	+	97.0771i	−69.6619	−	40.2193i	−169.126	−	58.2188i
2.2	−5.71329	+	1.53087i	−15.4449	−	4.13845i	16.4417	−	9.49261i	−22.7561	−	10.3519i	94.5767			−15.2970	+	46.5511i	−12.4854	+	12.4854i	151.270	+	87.3360i	145.859	+	24.3067i
2.3	−5.55079	+	1.48733i	15.0503	+	4.03273i	14.7427	−	8.51169i	−2.87000	−	24.8347i	−89.5393			40.0414	+	28.2434i	−4.15850	+	4.15850i	140.102	+	80.8879i	52.8682	+	133.584i
2.4	−5.20038	+	1.39344i	2.56504	+	0.687301i	11.2458	−	6.49278i	−19.5926	+	15.5283i	−14.2969			20.1640	−	44.6589i	11.4758	−	11.4758i	−64.0410	−	36.9741i	80.2514	−	108.054i
2.5	−3.07295	+	0.823393i	−9.80023	−	2.62596i	−5.09139	+	2.93952i	24.9768	+	1.07725i	32.2778			46.2809	−	16.0958i	49.2180	−	49.2180i	19.0008	+	10.9701i	−77.6393	+	17.2554i
2.6	−1.93554	+	0.518627i	0.952096	+	0.255113i	−10.3791	+	5.99235i	3.12714	−	24.8036i	−1.97513			−47.7288	−	11.0890i	39.6520	−	39.6520i	−69.3067	−	40.0142i	6.81113	+	49.6304i
2.7	−0.495094	+	0.132660i	15.4296	+	4.13434i	−13.6289	+	7.86864i	12.6360	+	21.5715i	−8.18755			−36.5078	−	32.6831i	11.5027	−	11.5027i	150.831	+	87.0822i	−9.11771	−	9.00363i
2.8	−0.167922	+	0.0449946i	2.09038	+	0.560116i	−13.8302	+	7.98489i	−20.4734	+	14.3471i	−0.376224			20.9813	+	44.2807i	3.92997	−	3.92997i	−66.0921	−	38.1583i	2.79240	−	3.33039i
2.9	2.34674	−	0.628807i	−11.5823	−	3.10347i	−8.74462	+	5.04871i	11.4928	+	22.2017i	−29.1322			−36.0021	+	33.2392i	−44.8336	+	44.8336i	54.3705	+	31.3908i	40.9311	+	44.8749i
2.10	3.05908	−	0.819678i	−10.5242	−	2.81996i	−5.17031	+	2.98508i	−19.9856	−	15.0191i	−34.5059			9.03266	−	48.1603i	−49.2000	+	49.2000i	32.6590	+	18.8557i	−73.4485	−	29.5629i
2.11	3.33928	−	0.894758i	6.96176	+	1.86540i	−3.50620	+	2.02430i	21.4576	−	12.8286i	24.9163			48.0380	+	9.66157i	−49.0093	+	49.0093i	−25.1617	−	14.5271i	60.1743	−	62.0376i
2.12	5.58177	−	1.49563i	11.2270	+	3.00826i	15.0628	−	8.69652i	−22.0427	−	11.7949i	67.1656			−38.6780	+	30.0834i	5.69217	−	5.69217i	46.8474	+	27.0474i	−140.678	−	32.8685i
2.13	6.17220	−	1.65384i	2.01200	+	0.539113i	21.5045	−	12.4156i	3.38702	+	24.7695i	13.3101			2.59467	−	48.9313i	39.9028	−	39.9028i	−66.3906	−	38.3306i	61.8701	+	147.281i
2.14	7.18170	−	1.92433i	−11.0263	−	2.95448i	34.0173	−	19.6399i	13.9161	−	20.7688i	−84.8726			−4.26291	+	48.8142i	122.391	−	122.391i	42.7013	+	24.6536i	59.9749	−	175.934i
18.1	−6.91084	−	1.85175i	0.723742	−	0.193926i	30.4743	+	17.5943i	20.7271	−	13.9781i	−5.36076			−44.7877	−	19.8761i	−97.0771	−	97.0771i	−69.6619	+	40.2193i	−169.126	+	58.2188i
18.2	−5.71329	−	1.53087i	−15.4449	+	4.13845i	16.4417	+	9.49261i	−22.7561	+	10.3519i	94.5767			−15.2970	−	46.5511i	−12.4854	−	12.4854i	151.270	−	87.3360i	145.859	−	24.3067i
18.3	−5.55079	−	1.48733i	15.0503	−	4.03273i	14.7427	+	8.51169i	−2.87000	+	24.8347i	−89.5393			40.0414	−	28.2434i	−4.15850	−	4.15850i	140.102	−	80.8879i	52.8682	−	133.584i
18.4	−5.20038	−	1.39344i	2.56504	−	0.687301i	11.2458	+	6.49278i	−19.5926	−	15.5283i	−14.2969			20.1640	+	44.6589i	11.4758	+	11.4758i	−64.0410	+	36.9741i	80.2514	+	108.054i
18.5	−3.07295	−	0.823393i	−9.80023	+	2.62596i	−5.09139	−	2.93952i	24.9768	−	1.07725i	32.2778			46.2809	+	16.0958i	49.2180	+	49.2180i	19.0008	−	10.9701i	−77.6393	−	17.2554i
18.6	−1.93554	−	0.518627i	0.952096	−	0.255113i	−10.3791	−	5.99235i	3.12714	+	24.8036i	−1.97513			−47.7288	+	11.0890i	39.6520	+	39.6520i	−69.3067	+	40.0142i	6.81113	−	49.6304i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
7.c	even	3	1	inner
35.l	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	35.5.l.a	✓	56
5.c	odd	4	1	inner	35.5.l.a	✓	56
7.c	even	3	1	inner	35.5.l.a	✓	56
35.l	odd	12	1	inner	35.5.l.a	✓	56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
35.5.l.a	✓	56	1.a	even	1	1	trivial
35.5.l.a	✓	56	5.c	odd	4	1	inner
35.5.l.a	✓	56	7.c	even	3	1	inner
35.5.l.a	✓	56	35.l	odd	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(35, [\chi])\).