Newform orbit 696.2.v.c

• Label: 696.2.v.c
• Level: $696$
• Weight: $2$
• Character orbit: 696.v
• Analytic conductor: $5.558$
• Analytic rank: $0$
• Dimension: $112$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 696 = 2^{3} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	696.v (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.55758798068\)
Analytic rank:	\(0\)
Dimension:	\(112\)
Relative dimension:	\(56\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 112 q - 4 q^{2} - 4 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
307.1	−1.40949	−	0.115545i	−0.707107	+	0.707107i	1.97330	+	0.325717i	0.914898			1.07836	−	0.914954i		−	4.64436i	−2.74370	−	0.687098i		−	1.00000i	−1.28954	−	0.105712i
307.2	−1.40075	+	0.194704i	0.707107	−	0.707107i	1.92418	−	0.545462i	2.43807			−0.852801	+	1.12815i		−	1.12011i	−2.58908	+	1.13870i		−	1.00000i	−3.41512	+	0.474703i
307.3	−1.39968	−	0.202251i	0.707107	−	0.707107i	1.91819	+	0.566173i	0.751694			−1.13273	+	0.846707i			2.88068i	−2.57033	−	1.18042i		−	1.00000i	−1.05213	−	0.152031i
307.4	−1.39753	−	0.216562i	−0.707107	+	0.707107i	1.90620	+	0.605305i	−3.59364			1.14134	−	0.835073i			4.12883i	−2.53290	−	1.25874i		−	1.00000i	5.02223	+	0.778245i
307.5	−1.38434	+	0.289127i	−0.707107	+	0.707107i	1.83281	−	0.800501i	−1.66891			0.774435	−	1.18332i			0.0910775i	−2.30579	+	1.63808i		−	1.00000i	2.31034	−	0.482526i
307.6	−1.35103	+	0.417999i	0.707107	−	0.707107i	1.65055	−	1.12946i	−4.03267			−0.659751	+	1.25089i			1.50213i	−1.75783	+	2.21586i		−	1.00000i	5.44825	−	1.68565i
307.7	−1.31361	−	0.523851i	0.707107	−	0.707107i	1.45116	+	1.37627i	−1.34369			−1.29928	+	0.558447i			1.54494i	−1.18530	−	2.56808i		−	1.00000i	1.76510	+	0.703895i
307.8	−1.30398	+	0.547383i	−0.707107	+	0.707107i	1.40074	−	1.42756i	4.18816			0.534998	−	1.30911i			4.32414i	−1.04513	+	2.62825i		−	1.00000i	−5.46129	+	2.29253i
307.9	−1.22357	−	0.709146i	−0.707107	+	0.707107i	0.994224	+	1.73537i	1.69357			1.36663	−	0.363749i			2.91721i	0.0141357	−	2.82839i		−	1.00000i	−2.07219	−	1.20099i
307.10	−1.20093	−	0.746834i	0.707107	−	0.707107i	0.884479	+	1.79379i	2.18989			−1.37728	+	0.321097i		−	4.74487i	0.277465	−	2.81478i		−	1.00000i	−2.62991	−	1.63549i
307.11	−1.14309	+	0.832671i	0.707107	−	0.707107i	0.613318	−	1.90364i	−0.619588			−0.219501	+	1.39708i		−	4.00262i	0.884026	+	2.68673i		−	1.00000i	0.708245	−	0.515913i
307.12	−1.12134	−	0.861738i	−0.707107	+	0.707107i	0.514814	+	1.93261i	0.214264			1.40225	−	0.183567i		−	2.94783i	1.08812	−	2.61075i		−	1.00000i	−0.240263	−	0.184640i
307.13	−1.08957	+	0.901575i	−0.707107	+	0.707107i	0.374324	−	1.96466i	−0.840456			0.132932	−	1.40795i			1.04307i	1.36343	+	2.47811i		−	1.00000i	0.915736	−	0.757734i
307.14	−1.04313	+	0.954927i	0.707107	−	0.707107i	0.176228	−	1.99222i	1.92033			−0.0623665	+	1.41284i			2.15391i	1.71860	+	2.24642i		−	1.00000i	−2.00315	+	1.83377i
307.15	−1.02585	−	0.973461i	0.707107	−	0.707107i	0.104746	+	1.99726i	3.90048			−1.41373	+	0.0370461i			4.15508i	1.83680	−	2.15086i		−	1.00000i	−4.00132	−	3.79697i
307.16	−1.00471	−	0.995267i	0.707107	−	0.707107i	0.0188853	+	1.99991i	−3.16364			−1.41420	+	0.00667704i		−	2.49164i	1.97147	−	2.02813i		−	1.00000i	3.17854	+	3.14867i
307.17	−0.954927	+	1.04313i	0.707107	−	0.707107i	−0.176228	−	1.99222i	−1.92033			0.0623665	+	1.41284i		−	2.15391i	2.24642	+	1.71860i		−	1.00000i	1.83377	−	2.00315i
307.18	−0.901575	+	1.08957i	−0.707107	+	0.707107i	−0.374324	−	1.96466i	0.840456			−0.132932	−	1.40795i		−	1.04307i	2.47811	+	1.36343i		−	1.00000i	−0.757734	+	0.915736i
307.19	−0.876445	−	1.10988i	−0.707107	+	0.707107i	−0.463687	+	1.94551i	−3.20419			1.40455	+	0.165066i		−	0.825599i	2.56568	−	1.19049i		−	1.00000i	2.80830	+	3.55628i
307.20	−0.832671	+	1.14309i	0.707107	−	0.707107i	−0.613318	−	1.90364i	0.619588			0.219501	+	1.39708i			4.00262i	2.68673	+	0.884026i		−	1.00000i	−0.515913	+	0.708245i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.d	odd	2	1	inner
29.c	odd	4	1	inner
232.k	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	696.2.v.c	✓	112
8.d	odd	2	1	inner	696.2.v.c	✓	112
29.c	odd	4	1	inner	696.2.v.c	✓	112
232.k	even	4	1	inner	696.2.v.c	✓	112

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
696.2.v.c	✓	112	1.a	even	1	1	trivial
696.2.v.c	✓	112	8.d	odd	2	1	inner
696.2.v.c	✓	112	29.c	odd	4	1	inner
696.2.v.c	✓	112	232.k	even	4	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^56 - 182*T5^54 + 15527*T5^52 - 825636*T5^50 + 30692759*T5^48 - 848132678*T5^46 + 18083861049*T5^44 - 304868906704*T5^42 + 4131419204920*T5^40 - 45513305575344*T5^38 + 410663849132304*T5^36 - 3048967867918208*T5^34 + 18669606733995232*T5^32 - 94310374221528832*T5^30 + 392422962671902336*T5^28 - 1340525285670175488*T5^26 + 3740092930286686976*T5^24 - 8462148486724826624*T5^22 + 15381785919790801152*T5^20 - 22195451226648387584*T5^18 + 25042484951534944256*T5^16 - 21673303320237875200*T5^14 + 14038840185368371200*T5^12 - 6587954299161116672*T5^10 + 2139583359889965056*T5^8 - 448562389883813888*T5^6 + 53987573081112576*T5^4 - 3004824678825984*T5^2 + 59281622695936