Newform orbit 1815.2.c.j

• Label: 1815.2.c.j
• Level: $1815$
• Weight: $2$
• Character orbit: 1815.c
• Analytic conductor: $14.493$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.4928479669\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{4} - 2 q^{5} - 8 q^{6} - 24 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
364.1		−	2.72592i		−	1.00000i	−5.43063			1.85250	+	1.25229i	−2.72592				−	0.486331i			9.35163i	−1.00000			3.41365	−	5.04977i
364.2		−	2.59201i		−	1.00000i	−4.71851			−0.0953833	−	2.23403i	−2.59201				−	3.41835i			7.04639i	−1.00000			−5.79063	+	0.247234i
364.3		−	2.36377i			1.00000i	−3.58741			0.979185	−	2.01027i	2.36377					1.71423i			3.75227i	−1.00000			−4.75182	−	2.31457i
364.4		−	2.21395i			1.00000i	−2.90157			−2.14116	−	0.644543i	2.21395					1.59339i			1.99602i	−1.00000			−1.42699	+	4.74042i
364.5		−	2.10651i		−	1.00000i	−2.43738			−0.823234	+	2.07901i	−2.10651					3.31633i			0.921348i	−1.00000			4.37946	+	1.73415i
364.6		−	1.90743i		−	1.00000i	−1.63829			−2.10308	−	0.759628i	−1.90743				−	4.45734i		−	0.689943i	−1.00000			−1.44894	+	4.01149i
364.7		−	1.27093i			1.00000i	0.384732			1.01340	+	1.99324i	1.27093				−	0.483291i		−	3.03083i	−1.00000			2.53328	−	1.28796i
364.8		−	0.803366i		−	1.00000i	1.35460			2.13623	+	0.660705i	−0.803366					0.508505i		−	2.69497i	−1.00000			0.530788	−	1.71617i
364.9		−	0.784131i			1.00000i	1.38514			−1.83964	−	1.27111i	0.784131					1.51801i		−	2.65439i	−1.00000			−0.996719	+	1.44252i
364.10		−	0.488299i		−	1.00000i	1.76156			2.10928	+	0.742259i	−0.488299				−	5.10895i		−	1.83677i	−1.00000			0.362444	−	1.02996i
364.11		−	0.298064i		−	1.00000i	1.91116			−1.68093	−	1.47460i	−0.298064					2.32107i		−	1.16578i	−1.00000			−0.439527	+	0.501026i
364.12		−	0.288813i			1.00000i	1.91659			−0.407156	+	2.19869i	0.288813				−	3.66740i		−	1.13116i	−1.00000			0.635009	+	0.117592i
364.13			0.288813i		−	1.00000i	1.91659			−0.407156	−	2.19869i	0.288813					3.66740i			1.13116i	−1.00000			0.635009	−	0.117592i
364.14			0.298064i			1.00000i	1.91116			−1.68093	+	1.47460i	−0.298064				−	2.32107i			1.16578i	−1.00000			−0.439527	−	0.501026i
364.15			0.488299i			1.00000i	1.76156			2.10928	−	0.742259i	−0.488299					5.10895i			1.83677i	−1.00000			0.362444	+	1.02996i
364.16			0.784131i		−	1.00000i	1.38514			−1.83964	+	1.27111i	0.784131				−	1.51801i			2.65439i	−1.00000			−0.996719	−	1.44252i
364.17			0.803366i			1.00000i	1.35460			2.13623	−	0.660705i	−0.803366				−	0.508505i			2.69497i	−1.00000			0.530788	+	1.71617i
364.18			1.27093i		−	1.00000i	0.384732			1.01340	−	1.99324i	1.27093					0.483291i			3.03083i	−1.00000			2.53328	+	1.28796i
364.19			1.90743i			1.00000i	−1.63829			−2.10308	+	0.759628i	−1.90743					4.45734i			0.689943i	−1.00000			−1.44894	−	4.01149i
364.20			2.10651i			1.00000i	−2.43738			−0.823234	−	2.07901i	−2.10651				−	3.31633i		−	0.921348i	−1.00000			4.37946	−	1.73415i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1815.2.c.j		24
5.b	even	2	1	inner	1815.2.c.j		24
5.c	odd	4	1		9075.2.a.dy		12
5.c	odd	4	1		9075.2.a.dz		12
11.b	odd	2	1		1815.2.c.k		24
11.c	even	5	2		165.2.s.a	✓	48
33.h	odd	10	2		495.2.ba.c		48
55.d	odd	2	1		1815.2.c.k		24
55.e	even	4	1		9075.2.a.dx		12
55.e	even	4	1		9075.2.a.ea		12
55.j	even	10	2		165.2.s.a	✓	48
55.k	odd	20	2		825.2.n.o		24
55.k	odd	20	2		825.2.n.p		24
165.o	odd	10	2		495.2.ba.c		48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
165.2.s.a	✓	48	11.c	even	5	2
165.2.s.a	✓	48	55.j	even	10	2
495.2.ba.c		48	33.h	odd	10	2
495.2.ba.c		48	165.o	odd	10	2
825.2.n.o		24	55.k	odd	20	2
825.2.n.p		24	55.k	odd	20	2
1815.2.c.j		24	1.a	even	1	1	trivial
1815.2.c.j		24	5.b	even	2	1	inner
1815.2.c.k		24	11.b	odd	2	1
1815.2.c.k		24	55.d	odd	2	1
9075.2.a.dx		12	55.e	even	4	1
9075.2.a.dy		12	5.c	odd	4	1
9075.2.a.dz		12	5.c	odd	4	1
9075.2.a.ea		12	55.e	even	4	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1815, [\chi])\):

T2^24 + 36*T2^22 + 552*T2^20 + 4702*T2^18 + 24334*T2^16 + 78666*T2^14 + 157743*T2^12 + 190094*T2^10 + 131587*T2^8 + 49704*T2^6 + 9451*T2^4 + 810*T2^2 + 25

T19^12 - 16*T19^11 + 16*T19^10 + 942*T19^9 - 4470*T19^8 - 10358*T19^7 + 106375*T19^6 - 137110*T19^5 - 402597*T19^4 + 947592*T19^3 + 51211*T19^2 - 1279690*T19 + 734525