Newform orbit 1694.2.c.c

• Label: 1694.2.c.c
• Level: $1694$
• Weight: $2$
• Character orbit: 1694.c
• Analytic conductor: $13.527$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1694 = 2 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1694.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(13.5266581024\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Twist minimal:	no (minimal twist has level 154)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 32 q^{4} - 24 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1693.1		−	1.00000i			2.80203i	−1.00000					1.33392i	2.80203			−0.0642082	−	2.64497i			1.00000i	−4.85135			1.33392
1693.2		−	1.00000i		−	2.80203i	−1.00000				−	1.33392i	−2.80203			0.0642082	−	2.64497i			1.00000i	−4.85135			−1.33392
1693.3			1.00000i		−	2.80203i	−1.00000				−	1.33392i	2.80203			−0.0642082	+	2.64497i		−	1.00000i	−4.85135			1.33392
1693.4			1.00000i			2.80203i	−1.00000					1.33392i	−2.80203			0.0642082	+	2.64497i		−	1.00000i	−4.85135			−1.33392
1693.5		−	1.00000i			0.328992i	−1.00000					4.30373i	0.328992			−1.36668	+	2.26544i			1.00000i	2.89176			4.30373
1693.6		−	1.00000i		−	0.328992i	−1.00000				−	4.30373i	−0.328992			1.36668	+	2.26544i			1.00000i	2.89176			−4.30373
1693.7			1.00000i		−	0.328992i	−1.00000				−	4.30373i	0.328992			−1.36668	−	2.26544i		−	1.00000i	2.89176			4.30373
1693.8			1.00000i			0.328992i	−1.00000					4.30373i	−0.328992			1.36668	−	2.26544i		−	1.00000i	2.89176			−4.30373
1693.9		−	1.00000i		−	1.98055i	−1.00000					0.684352i	−1.98055			2.34424	−	1.22659i			1.00000i	−0.922589			0.684352
1693.10		−	1.00000i			1.98055i	−1.00000				−	0.684352i	1.98055			−2.34424	−	1.22659i			1.00000i	−0.922589			−0.684352
1693.11			1.00000i			1.98055i	−1.00000				−	0.684352i	−1.98055			2.34424	+	1.22659i		−	1.00000i	−0.922589			0.684352
1693.12			1.00000i		−	1.98055i	−1.00000					0.684352i	1.98055			−2.34424	+	1.22659i		−	1.00000i	−0.922589			−0.684352
1693.13		−	1.00000i		−	2.92469i	−1.00000					2.69327i	−2.92469			−2.37622	+	1.16344i			1.00000i	−5.55379			2.69327
1693.14		−	1.00000i			2.92469i	−1.00000				−	2.69327i	2.92469			2.37622	+	1.16344i			1.00000i	−5.55379			−2.69327
1693.15			1.00000i			2.92469i	−1.00000				−	2.69327i	−2.92469			−2.37622	−	1.16344i		−	1.00000i	−5.55379			2.69327
1693.16			1.00000i		−	2.92469i	−1.00000					2.69327i	2.92469			2.37622	−	1.16344i		−	1.00000i	−5.55379			−2.69327
1693.17		−	1.00000i			0.939017i	−1.00000				−	1.41215i	0.939017			2.57538	+	0.606130i			1.00000i	2.11825			−1.41215
1693.18		−	1.00000i		−	0.939017i	−1.00000					1.41215i	−0.939017			−2.57538	+	0.606130i			1.00000i	2.11825			1.41215
1693.19			1.00000i		−	0.939017i	−1.00000					1.41215i	0.939017			2.57538	−	0.606130i		−	1.00000i	2.11825			−1.41215
1693.20			1.00000i			0.939017i	−1.00000				−	1.41215i	−0.939017			−2.57538	−	0.606130i		−	1.00000i	2.11825			1.41215

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
11.b	odd	2	1	inner
77.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1694.2.c.c		32
7.b	odd	2	1	inner	1694.2.c.c		32
11.b	odd	2	1	inner	1694.2.c.c		32
11.c	even	5	1		154.2.k.a	✓	32
11.d	odd	10	1		154.2.k.a	✓	32
77.b	even	2	1	inner	1694.2.c.c		32
77.j	odd	10	1		154.2.k.a	✓	32
77.l	even	10	1		154.2.k.a	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
154.2.k.a	✓	32	11.c	even	5	1
154.2.k.a	✓	32	11.d	odd	10	1
154.2.k.a	✓	32	77.j	odd	10	1
154.2.k.a	✓	32	77.l	even	10	1
1694.2.c.c		32	1.a	even	1	1	trivial
1694.2.c.c		32	7.b	odd	2	1	inner
1694.2.c.c		32	11.b	odd	2	1	inner
1694.2.c.c		32	77.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{16} + 30T_{3}^{14} + 361T_{3}^{12} + 2250T_{3}^{10} + 7836T_{3}^{8} + 15230T_{3}^{6} + 15341T_{3}^{4} + 6490T_{3}^{2} + 541 \) acting on \(S_{2}^{\mathrm{new}}(1694, [\chi])\).