Newform orbit 2496.4.a.v

• Label: 2496.4.a.v
• Level: $2496$
• Weight: $4$
• Character orbit: 2496.a
• Self dual: yes
• Analytic conductor: $147.269$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$2496 = 2^{6} \cdot 3 \cdot 13$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	2496.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$147.268767374$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{113})$
Defining polynomial:	$x^{2} - x - 28$
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$2$
Twist minimal:	no (minimal twist has level 312)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the $q$-expansion are expressed in terms of $\beta = \sqrt{113}$. We also show the integral $q$-expansion of the trace form.

$f(q)$	$=$	q - 3 * q^3 + (-b - 3) * q^5 + (b + 5) * q^7 + 9 * q^9 + (-4*b - 8) * q^11 - 13 * q^13 + (3*b + 9) * q^15 + 2 * q^17 + (5*b - 35) * q^19 + (-3*b - 15) * q^21 + 64 * q^23 + (6*b - 3) * q^25 - 27 * q^27 + (6*b + 40) * q^29 + (-15*b + 125) * q^31 + (12*b + 24) * q^33 + (-8*b - 128) * q^35 + (18*b + 76) * q^37 + 39 * q^39 + (-7*b - 73) * q^41 + (8*b - 252) * q^43 + (-9*b - 27) * q^45 + (6*b + 262) * q^47 + (10*b - 205) * q^49 - 6 * q^51 + (8*b + 26) * q^53 + (20*b + 476) * q^55 + (-15*b + 105) * q^57 + (10*b - 82) * q^59 + (46*b + 152) * q^61 + (9*b + 45) * q^63 + (13*b + 39) * q^65 + (7*b - 457) * q^67 - 192 * q^69 - 48*b * q^71 + (-6*b - 228) * q^73 + (-18*b + 9) * q^75 + (-28*b - 492) * q^77 + (36*b + 412) * q^79 + 81 * q^81 + (50*b + 414) * q^83 + (-2*b - 6) * q^85 + (-18*b - 120) * q^87 + (-9*b + 413) * q^89 + (-13*b - 65) * q^91 + (45*b - 375) * q^93 + (20*b - 460) * q^95 + (122*b + 276) * q^97 + (-36*b - 72) * q^99
$\operatorname{Tr}(f)(q)$	$=$	2 * q - 6 * q^3 - 6 * q^5 + 10 * q^7 + 18 * q^9 - 16 * q^11 - 26 * q^13 + 18 * q^15 + 4 * q^17 - 70 * q^19 - 30 * q^21 + 128 * q^23 - 6 * q^25 - 54 * q^27 + 80 * q^29 + 250 * q^31 + 48 * q^33 - 256 * q^35 + 152 * q^37 + 78 * q^39 - 146 * q^41 - 504 * q^43 - 54 * q^45 + 524 * q^47 - 410 * q^49 - 12 * q^51 + 52 * q^53 + 952 * q^55 + 210 * q^57 - 164 * q^59 + 304 * q^61 + 90 * q^63 + 78 * q^65 - 914 * q^67 - 384 * q^69 - 456 * q^73 + 18 * q^75 - 984 * q^77 + 824 * q^79 + 162 * q^81 + 828 * q^83 - 12 * q^85 - 240 * q^87 + 826 * q^89 - 130 * q^91 - 750 * q^93 - 920 * q^95 + 552 * q^97 - 144 * 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

5.81507
−4.81507

0

−3.00000

0

−13.6301

0

15.6301

0

9.00000

0

1.2

0

−3.00000

0

7.63015

0

−5.63015

0

9.00000

0

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$+1$
$13$	$+1$

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	2496.4.a.v		2
4.b	odd	2	1		2496.4.a.be		2
8.b	even	2	1		624.4.a.q		2
8.d	odd	2	1		312.4.a.c	✓	2
24.f	even	2	1		936.4.a.d		2
24.h	odd	2	1		1872.4.a.x		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
312.4.a.c	✓	2	8.d	odd	2	1
624.4.a.q		2	8.b	even	2	1
936.4.a.d		2	24.f	even	2	1
1872.4.a.x		2	24.h	odd	2	1
2496.4.a.v		2	1.a	even	1	1	trivial
2496.4.a.be		2	4.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 $S_{4}^{\mathrm{new}}(\Gamma_0(2496))$:

$T_{5}^{2} + 6T_{5} - 104$

$T_{7}^{2} - 10T_{7} - 88$

$T_{11}^{2} + 16T_{11} - 1744$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T^{2}$
$3$	$(T + 3)^{2}$
$5$	$T^{2} + 6T - 104$
$7$	$T^{2} - 10T - 88$
$11$	$T^{2} + 16T - 1744$