Newform orbit 828.4.a.d

• Label: 828.4.a.d
• 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:	\(\Z[a_1, \ldots, a_{5}]\)
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 + (b + 1) * q^5 + 2 * q^7 + (-7*b - 7) * q^11 + (10*b - 12) * q^13 + (10*b + 10) * q^17 + (-35*b - 9) * q^19 + 23 * q^23 + (2*b - 111) * q^25 + (-22*b + 116) * q^29 + (38*b - 146) * q^31 + (2*b + 2) * q^35 + (45*b - 205) * q^37 + (12*b + 150) * q^41 + (-77*b - 99) * q^43 + (-72*b + 60) * q^47 - 339 * q^49 + (125*b + 113) * q^53 + (-14*b - 98) * q^55 + (-144*b - 12) * q^59 + (-29*b - 231) * q^61 + (-2*b + 118) * q^65 + (9*b + 95) * q^67 + (240*b - 324) * q^71 + (26*b - 320) * q^73 + (-14*b - 14) * q^77 + (104*b - 314) * q^79 + (119*b - 865) * q^83 + (20*b + 140) * q^85 + (-96*b + 36) * q^89 + (20*b - 24) * q^91 + (-44*b - 464) * q^95 + (-106*b - 380) * q^97
\(\operatorname{Tr}(f)(q)\)	\(=\)	2 * q + 2 * q^5 + 4 * q^7 - 14 * q^11 - 24 * q^13 + 20 * q^17 - 18 * q^19 + 46 * q^23 - 222 * q^25 + 232 * q^29 - 292 * q^31 + 4 * q^35 - 410 * q^37 + 300 * q^41 - 198 * q^43 + 120 * q^47 - 678 * q^49 + 226 * q^53 - 196 * q^55 - 24 * q^59 - 462 * q^61 + 236 * q^65 + 190 * q^67 - 648 * q^71 - 640 * q^73 - 28 * q^77 - 628 * q^79 - 1730 * q^83 + 280 * q^85 + 72 * q^89 - 48 * q^91 - 928 * q^95 - 760 * 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

−1.30278
2.30278

0

0

0

−2.60555

0

2.00000

0

0

0

1.2

0

0

0

4.60555

0

2.00000

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

    

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{2} - 2T_{5} - 12 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(828))\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} \)
$5$	\( T^{2} - 2T - 12 \)
$7$	\( (T - 2)^{2} \)
$11$	\( T^{2} + 14T - 588 \)