Newform orbit 546.4.a.a

• Label: 546.4.a.a
• Level: $546$
• Weight: $4$
• Character orbit: 546.a
• Self dual: yes
• Analytic conductor: $32.215$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(32.2150428631\)
Analytic rank:	\(1\)
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 + 4 * q^4 + 12 * q^5 + 6 * q^6 + 7 * q^7 - 8 * q^8 + 9 * q^9 - 24 * q^10 - 22 * q^11 - 12 * q^12 - 13 * q^13 - 14 * q^14 - 36 * q^15 + 16 * q^16 - 2 * q^17 - 18 * q^18 - 88 * q^19 + 48 * q^20 - 21 * q^21 + 44 * q^22 - 80 * q^23 + 24 * q^24 + 19 * q^25 + 26 * q^26 - 27 * q^27 + 28 * q^28 - 22 * q^29 + 72 * q^30 - 92 * q^31 - 32 * q^32 + 66 * q^33 + 4 * q^34 + 84 * q^35 + 36 * q^36 + 118 * q^37 + 176 * q^38 + 39 * q^39 - 96 * q^40 + 324 * q^41 + 42 * q^42 + 84 * q^43 - 88 * q^44 + 108 * q^45 + 160 * q^46 - 134 * q^47 - 48 * q^48 + 49 * q^49 - 38 * q^50 + 6 * q^51 - 52 * q^52 - 194 * q^53 + 54 * q^54 - 264 * q^55 - 56 * q^56 + 264 * q^57 + 44 * q^58 + 210 * q^59 - 144 * q^60 - 470 * q^61 + 184 * q^62 + 63 * q^63 + 64 * q^64 - 156 * q^65 - 132 * q^66 - 292 * q^67 - 8 * q^68 + 240 * q^69 - 168 * q^70 - 66 * q^71 - 72 * q^72 - 506 * q^73 - 236 * q^74 - 57 * q^75 - 352 * q^76 - 154 * q^77 - 78 * q^78 - 776 * q^79 + 192 * q^80 + 81 * q^81 - 648 * q^82 - 778 * q^83 - 84 * q^84 - 24 * q^85 - 168 * q^86 + 66 * q^87 + 176 * q^88 - 920 * q^89 - 216 * q^90 - 91 * q^91 - 320 * q^92 + 276 * q^93 + 268 * q^94 - 1056 * q^95 + 96 * q^96 - 490 * q^97 - 98 * q^98 - 198 * q^99

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

4.00000

12.0000

6.00000

7.00000

−8.00000

9.00000

−24.0000

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( +1 \)
\(3\)	\( +1 \)
\(7\)	\( -1 \)
\(13\)	\( +1 \)

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	546.4.a.a	✓	1
3.b	odd	2	1		1638.4.a.i		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
546.4.a.a	✓	1	1.a	even	1	1	trivial
1638.4.a.i		1	3.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} - 12 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(546))\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T + 2 \)
$3$	\( T + 3 \)
$5$	\( T - 12 \)
$7$	\( T - 7 \)
$11$	\( T + 22 \)