Newform orbit 828.4.a.c

• Label: 828.4.a.c
• Level: $828$
• Weight: $4$
• Character orbit: 828.a
• Self dual: yes
• Analytic conductor: $48.854$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	828.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(48.8535814848\)
Analytic rank:	\(1\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{13}) \)
Defining polynomial:	\( x^{2} - x - 3 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index:	\( 2 \)
Twist minimal:	no (minimal twist has level 276)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{13}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	q + (-3*b - 7) * q^5 + (b - 5) * q^7 + (2*b + 2) * q^11 + (6*b + 52) * q^13 + (15*b - 61) * q^17 + (-21*b + 37) * q^19 + 23 * q^23 + (42*b + 41) * q^25 + (54*b - 20) * q^29 + (-50*b + 2) * q^31 + (8*b - 4) * q^35 + (12*b + 170) * q^37 + (-104*b - 82) * q^41 + (115*b - 3) * q^43 + (80*b - 284) * q^47 + (-10*b - 305) * q^49 + (-17*b - 225) * q^53 + (-20*b - 92) * q^55 + (-40*b - 200) * q^59 + (-176*b + 150) * q^61 + (-198*b - 598) * q^65 + (81*b - 265) * q^67 + (84*b - 60) * q^71 + (-156*b - 234) * q^73 + (-8*b + 16) * q^77 + (-13*b - 863) * q^79 + (22*b - 690) * q^83 + (78*b - 158) * q^85 + (237*b + 261) * q^89 + (22*b - 182) * q^91 + (36*b + 560) * q^95 + (166*b + 20) * q^97
\(\operatorname{Tr}(f)(q)\)	\(=\)	2 * q - 14 * q^5 - 10 * q^7 + 4 * q^11 + 104 * q^13 - 122 * q^17 + 74 * q^19 + 46 * q^23 + 82 * q^25 - 40 * q^29 + 4 * q^31 - 8 * q^35 + 340 * q^37 - 164 * q^41 - 6 * q^43 - 568 * q^47 - 610 * q^49 - 450 * q^53 - 184 * q^55 - 400 * q^59 + 300 * q^61 - 1196 * q^65 - 530 * q^67 - 120 * q^71 - 468 * q^73 + 32 * q^77 - 1726 * q^79 - 1380 * q^83 - 316 * q^85 + 522 * q^89 - 364 * q^91 + 1120 * q^95 + 40 * q^97

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

2.30278
−1.30278

0

0

0

−17.8167

0

−1.39445

0

0

0

1.2

0

0

0

3.81665

0

−8.60555

0

0

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( -1 \)
\(3\)	\( -1 \)
\(23\)	\( -1 \)

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	828.4.a.c		2
3.b	odd	2	1		276.4.a.d	✓	2
12.b	even	2	1		1104.4.a.l		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
276.4.a.d	✓	2	3.b	odd	2	1
828.4.a.c		2	1.a	even	1	1	trivial
1104.4.a.l		2	12.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{2} + 14T_{5} - 68 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(828))\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} \)
$5$	\( T^{2} + 14T - 68 \)
$7$	\( T^{2} + 10T + 12 \)
$11$	\( T^{2} - 4T - 48 \)