Newform orbit 11.7.b.a

• Label: 11.7.b.a
• Level: $11$
• Weight: $7$
• Character orbit: 11.b
• Self dual: yes
• Analytic conductor: $2.531$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -11
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	11.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(2.53059491982\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\)

\(=\)

q + 10 * q^3 + 64 * q^4 + 74 * q^5 - 629 * q^9 - 1331 * q^11 + 640 * q^12 + 740 * q^15 + 4096 * q^16 + 4736 * q^20 - 12670 * q^23 - 10149 * q^25 - 13580 * q^27 + 56018 * q^31 - 13310 * q^33 - 40256 * q^36 + 87050 * q^37 - 85184 * q^44 - 46546 * q^45 - 206350 * q^47 + 40960 * q^48 + 117649 * q^49 + 246890 * q^53 - 98494 * q^55 + 107642 * q^59 + 47360 * q^60 + 262144 * q^64 - 428470 * q^67 - 126700 * q^69 - 341278 * q^71 - 101490 * q^75 + 303104 * q^80 + 322741 * q^81 + 1392338 * q^89 - 810880 * q^92 + 560180 * q^93 - 1824190 * q^97 + 837199 * q^99

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).

\(n\)	\(2\)
\(\chi(n)\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

10.1

0

0

10.0000

64.0000

74.0000

0

0

0

−629.000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.b	odd	2	1	CM by \(\Q(\sqrt{-11}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	11.7.b.a	✓	1
3.b	odd	2	1		99.7.c.a		1
4.b	odd	2	1		176.7.h.a		1
11.b	odd	2	1	CM	11.7.b.a	✓	1
33.d	even	2	1		99.7.c.a		1
44.c	even	2	1		176.7.h.a		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
11.7.b.a	✓	1	1.a	even	1	1	trivial
11.7.b.a	✓	1	11.b	odd	2	1	CM
99.7.c.a		1	3.b	odd	2	1
99.7.c.a		1	33.d	even	2	1
176.7.h.a		1	4.b	odd	2	1
176.7.h.a		1	44.c	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} \) acting on \(S_{7}^{\mathrm{new}}(11, [\chi])\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T \)
$3$	\( T - 10 \)
$5$	\( T - 74 \)
$7$	\( T \)
$11$	\( T + 1331 \)