Newform orbit 855.2.da.c

• Label: 855.2.da.c
• Level: $855$
• Weight: $2$
• Character orbit: 855.da
• Analytic conductor: $6.827$
• Analytic rank: $0$
• Dimension: $96$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.da (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.82720937282\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(16\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 96 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
199.1	−2.44017	+	0.430268i		0		3.88992	−	1.41581i	−1.18385	+	1.89697i		0		−3.88542	−	2.24325i	−4.59119	+	2.65072i		0		2.07259	−	5.13831i
199.2	−2.44017	+	0.430268i		0		3.88992	−	1.41581i	−0.312467	+	2.21413i		0		3.88542	+	2.24325i	−4.59119	+	2.65072i		0		−0.190196	−	5.53730i
199.3	−1.88977	+	0.333218i		0		1.58082	−	0.575373i	−2.03350	−	0.929980i		0		1.86561	+	1.07711i	0.528003	−	0.304842i		0		4.15275	+	1.07985i
199.4	−1.88977	+	0.333218i		0		1.58082	−	0.575373i	2.15553	+	0.594705i		0		−1.86561	−	1.07711i	0.528003	−	0.304842i		0		−4.27164	−	0.405594i
199.5	−1.01346	+	0.178700i		0		−0.884219	+	0.321829i	−2.13118	+	0.676823i		0		0.455113	+	0.262760i	2.62105	−	1.51326i		0		2.03891	−	1.06677i
199.6	−1.01346	+	0.178700i		0		−0.884219	+	0.321829i	1.19752	+	1.88837i		0		−0.455113	−	0.262760i	2.62105	−	1.51326i		0		−1.55109	−	1.69979i
199.7	−0.339897	+	0.0599330i		0		−1.76745	+	0.643298i	−2.07651	+	0.829529i		0		−2.36837	−	1.36738i	1.16000	−	0.669724i		0		0.656083	−	0.406406i
199.8	−0.339897	+	0.0599330i		0		−1.76745	+	0.643298i	1.05749	+	1.97021i		0		2.36837	+	1.36738i	1.16000	−	0.669724i		0		−0.477517	−	0.606290i
199.9	0.339897	−	0.0599330i		0		−1.76745	+	0.643298i	−1.05749	−	1.97021i		0		2.36837	+	1.36738i	−1.16000	+	0.669724i		0		−0.477517	−	0.606290i
199.10	0.339897	−	0.0599330i		0		−1.76745	+	0.643298i	2.07651	−	0.829529i		0		−2.36837	−	1.36738i	−1.16000	+	0.669724i		0		0.656083	−	0.406406i
199.11	1.01346	−	0.178700i		0		−0.884219	+	0.321829i	−1.19752	−	1.88837i		0		−0.455113	−	0.262760i	−2.62105	+	1.51326i		0		−1.55109	−	1.69979i
199.12	1.01346	−	0.178700i		0		−0.884219	+	0.321829i	2.13118	−	0.676823i		0		0.455113	+	0.262760i	−2.62105	+	1.51326i		0		2.03891	−	1.06677i
199.13	1.88977	−	0.333218i		0		1.58082	−	0.575373i	−2.15553	−	0.594705i		0		−1.86561	−	1.07711i	−0.528003	+	0.304842i		0		−4.27164	−	0.405594i
199.14	1.88977	−	0.333218i		0		1.58082	−	0.575373i	2.03350	+	0.929980i		0		1.86561	+	1.07711i	−0.528003	+	0.304842i		0		4.15275	+	1.07985i
199.15	2.44017	−	0.430268i		0		3.88992	−	1.41581i	0.312467	−	2.21413i		0		3.88542	+	2.24325i	4.59119	−	2.65072i		0		−0.190196	−	5.53730i
199.16	2.44017	−	0.430268i		0		3.88992	−	1.41581i	1.18385	−	1.89697i		0		−3.88542	−	2.24325i	4.59119	−	2.65072i		0		2.07259	−	5.13831i
244.1	−1.63349	+	1.94672i		0		−0.774122	−	4.39026i	1.32890	+	1.79834i		0		−4.00758	+	2.31378i	5.40953	+	3.12319i		0		−5.67160	−	0.350572i
244.2	−1.63349	+	1.94672i		0		−0.774122	−	4.39026i	1.86383	−	1.23537i		0		4.00758	−	2.31378i	5.40953	+	3.12319i		0		−0.639617	+	5.64631i
244.3	−1.26951	+	1.51294i		0		−0.330046	−	1.87178i	−0.00846887	+	2.23605i		0		1.82455	−	1.05340i	−0.169918	−	0.0981021i		0		−3.37227	−	2.85150i
244.4	−1.26951	+	1.51294i		0		−0.330046	−	1.87178i	0.756817	−	2.10410i		0		−1.82455	+	1.05340i	−0.169918	−	0.0981021i		0		2.22260	+	3.81620i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.b	even	2	1	inner
15.d	odd	2	1	inner
19.e	even	9	1	inner
57.l	odd	18	1	inner
95.p	even	18	1	inner
285.bd	odd	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	855.2.da.c	✓	96
3.b	odd	2	1	inner	855.2.da.c	✓	96
5.b	even	2	1	inner	855.2.da.c	✓	96
15.d	odd	2	1	inner	855.2.da.c	✓	96
19.e	even	9	1	inner	855.2.da.c	✓	96
57.l	odd	18	1	inner	855.2.da.c	✓	96
95.p	even	18	1	inner	855.2.da.c	✓	96
285.bd	odd	18	1	inner	855.2.da.c	✓	96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
855.2.da.c	✓	96	1.a	even	1	1	trivial
855.2.da.c	✓	96	3.b	odd	2	1	inner
855.2.da.c	✓	96	5.b	even	2	1	inner
855.2.da.c	✓	96	15.d	odd	2	1	inner
855.2.da.c	✓	96	19.e	even	9	1	inner
855.2.da.c	✓	96	57.l	odd	18	1	inner
855.2.da.c	✓	96	95.p	even	18	1	inner
855.2.da.c	✓	96	285.bd	odd	18	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^48 + 6*T2^44 - 269*T2^42 - 444*T2^40 + 1098*T2^38 + 59043*T2^36 + 85458*T2^34 - 12018*T2^32 - 3149568*T2^30 - 4526853*T2^28 + 2487870*T2^26 + 138854974*T2^24 + 136570320*T2^22 - 71468391*T2^20 - 269452206*T2^18 - 16680228*T2^16 + 138135309*T2^14 + 131648637*T2^12 + 32306100*T2^10 + 19317168*T2^8 - 1395712*T2^6 + 680064*T2^4 - 223584*T2^2 + 18496