Newform orbit 2299.2.a.a

• Label: 2299.2.a.a
• Level: $2299$
• Weight: $2$
• Character orbit: 2299.a
• Self dual: yes
• Analytic conductor: $18.358$
• Analytic rank: $2$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2299 = 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2299.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(18.3576074247\)
Analytic rank:	\(2\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	yes
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

q - 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^5 + 6 * q^6 - 2 * q^7 + 6 * q^9 + 6 * q^10 - 6 * q^12 - 2 * q^13 + 4 * q^14 + 9 * q^15 - 4 * q^16 - 6 * q^17 - 12 * q^18 + q^19 - 6 * q^20 + 6 * q^21 + 3 * q^23 + 4 * q^25 + 4 * q^26 - 9 * q^27 - 4 * q^28 + 10 * q^29 - 18 * q^30 + q^31 + 8 * q^32 + 12 * q^34 + 6 * q^35 + 12 * q^36 - 11 * q^37 - 2 * q^38 + 6 * q^39 - 8 * q^41 - 12 * q^42 - 4 * q^43 - 18 * q^45 - 6 * q^46 - 8 * q^47 + 12 * q^48 - 3 * q^49 - 8 * q^50 + 18 * q^51 - 4 * q^52 - 6 * q^53 + 18 * q^54 - 3 * q^57 - 20 * q^58 - q^59 + 18 * q^60 - 14 * q^61 - 2 * q^62 - 12 * q^63 - 8 * q^64 + 6 * q^65 - 13 * q^67 - 12 * q^68 - 9 * q^69 - 12 * q^70 - 13 * q^71 + 4 * q^73 + 22 * q^74 - 12 * q^75 + 2 * q^76 - 12 * q^78 - 10 * q^79 + 12 * q^80 + 9 * q^81 + 16 * q^82 + 6 * q^83 + 12 * q^84 + 18 * q^85 + 8 * q^86 - 30 * q^87 - 7 * q^89 + 36 * q^90 + 4 * q^91 + 6 * q^92 - 3 * q^93 + 16 * q^94 - 3 * q^95 - 24 * q^96 - 9 * q^97 + 6 * q^98

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1.1

0

−2.00000

−3.00000

2.00000

−3.00000

6.00000

−2.00000

0

6.00000

6.00000

Atkin-Lehner signs

\( p \)	Sign
\(11\)	\( +1 \)
\(19\)	\( -1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2299.2.a.a	✓	1
11.b	odd	2	1		2299.2.a.d	yes	1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2299.2.a.a	✓	1	1.a	even	1	1	trivial
2299.2.a.d	yes	1	11.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2299))\):

\( T_{2} + 2 \)

\( T_{3} + 3 \)

\( T_{7} + 2 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T + 2 \)
$3$	\( T + 3 \)
$5$	\( T + 3 \)
$7$	\( T + 2 \)
$11$	\( T \)