Newform orbit 2450.4.a.br

• Label: 2450.4.a.br
• Level: $2450$
• Weight: $4$
• Character orbit: 2450.a
• Self dual: yes
• Analytic conductor: $144.555$
• Analytic rank: $1$
• Dimension: $2$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2450.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(144.554679514\)
Analytic rank:	\(1\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{7}) \)
Defining polynomial:	\( x^{2} - 7 \)
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 2 \)
Twist minimal:	yes
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 2\sqrt{7}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	q - 2 * q^2 + b * q^3 + 4 * q^4 - 2*b * q^6 - 8 * q^8 + q^9 - 15 * q^11 + 4*b * q^12 + 3*b * q^13 + 16 * q^16 - 6*b * q^17 - 2 * q^18 + 16*b * q^19 + 30 * q^22 + 57 * q^23 - 8*b * q^24 - 6*b * q^26 - 26*b * q^27 - 71 * q^29 - 17*b * q^31 - 32 * q^32 - 15*b * q^33 + 12*b * q^34 + 4 * q^36 - 97 * q^37 - 32*b * q^38 + 84 * q^39 + 37*b * q^41 + 99 * q^43 - 60 * q^44 - 114 * q^46 - 62*b * q^47 + 16*b * q^48 - 168 * q^51 + 12*b * q^52 + 278 * q^53 + 52*b * q^54 + 448 * q^57 + 142 * q^58 + 19*b * q^59 - 41*b * q^61 + 34*b * q^62 + 64 * q^64 + 30*b * q^66 + 85 * q^67 - 24*b * q^68 + 57*b * q^69 + 41 * q^71 - 8 * q^72 - 141*b * q^73 + 194 * q^74 + 64*b * q^76 - 168 * q^78 - 785 * q^79 - 755 * q^81 - 74*b * q^82 + 229*b * q^83 - 198 * q^86 - 71*b * q^87 + 120 * q^88 + 195*b * q^89 + 228 * q^92 - 476 * q^93 + 124*b * q^94 - 32*b * q^96 + 35*b * q^97 - 15 * q^99
\(\operatorname{Tr}(f)(q)\)	\(=\)	2 * q - 4 * q^2 + 8 * q^4 - 16 * q^8 + 2 * q^9 - 30 * q^11 + 32 * q^16 - 4 * q^18 + 60 * q^22 + 114 * q^23 - 142 * q^29 - 64 * q^32 + 8 * q^36 - 194 * q^37 + 168 * q^39 + 198 * q^43 - 120 * q^44 - 228 * q^46 - 336 * q^51 + 556 * q^53 + 896 * q^57 + 284 * q^58 + 128 * q^64 + 170 * q^67 + 82 * q^71 - 16 * q^72 + 388 * q^74 - 336 * q^78 - 1570 * q^79 - 1510 * q^81 - 396 * q^86 + 240 * q^88 + 456 * q^92 - 952 * q^93 - 30 * 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

−2.64575
2.64575

−2.00000

−5.29150

4.00000

0

10.5830

0

−8.00000

1.00000

0

1.2

−2.00000

5.29150

4.00000

0

−10.5830

0

−8.00000

1.00000

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( +1 \)
\(5\)	\( +1 \)
\(7\)	\( -1 \)

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2450.4.a.br	✓	2
5.b	even	2	1		2450.4.a.bw	yes	2
7.b	odd	2	1	inner	2450.4.a.br	✓	2
35.c	odd	2	1		2450.4.a.bw	yes	2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2450.4.a.br	✓	2	1.a	even	1	1	trivial
2450.4.a.br	✓	2	7.b	odd	2	1	inner
2450.4.a.bw	yes	2	5.b	even	2	1
2450.4.a.bw	yes	2	35.c	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(2450))\):

\( T_{3}^{2} - 28 \)

\( T_{11} + 15 \)

\( T_{19}^{2} - 7168 \)

\( T_{23} - 57 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( (T + 2)^{2} \)
$3$	\( T^{2} - 28 \)
$5$	\( T^{2} \)
$7$	\( T^{2} \)
$11$	\( (T + 15)^{2} \)