Newform orbit 127.4.a.a

• Label: 127.4.a.a
• Level: $127$
• Weight: $4$
• Character orbit: 127.a
• Self dual: yes
• Analytic conductor: $7.493$
• Analytic rank: $2$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$127$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	127.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$7.49324257073$
Analytic rank:	$2$
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 - q^2 - 8 * q^3 - 7 * q^4 - 15 * q^5 + 8 * q^6 - 25 * q^7 + 15 * q^8 + 37 * q^9 + 15 * q^10 - 51 * q^11 + 56 * q^12 + 2 * q^13 + 25 * q^14 + 120 * q^15 + 41 * q^16 + 31 * q^17 - 37 * q^18 - 123 * q^19 + 105 * q^20 + 200 * q^21 + 51 * q^22 - 149 * q^23 - 120 * q^24 + 100 * q^25 - 2 * q^26 - 80 * q^27 + 175 * q^28 + 6 * q^29 - 120 * q^30 + 10 * q^31 - 161 * q^32 + 408 * q^33 - 31 * q^34 + 375 * q^35 - 259 * q^36 - 348 * q^37 + 123 * q^38 - 16 * q^39 - 225 * q^40 - 387 * q^41 - 200 * q^42 - 80 * q^43 + 357 * q^44 - 555 * q^45 + 149 * q^46 + 266 * q^47 - 328 * q^48 + 282 * q^49 - 100 * q^50 - 248 * q^51 - 14 * q^52 + 347 * q^53 + 80 * q^54 + 765 * q^55 - 375 * q^56 + 984 * q^57 - 6 * q^58 - 656 * q^59 - 840 * q^60 - 158 * q^61 - 10 * q^62 - 925 * q^63 - 167 * q^64 - 30 * q^65 - 408 * q^66 - 314 * q^67 - 217 * q^68 + 1192 * q^69 - 375 * q^70 + 312 * q^71 + 555 * q^72 - 646 * q^73 + 348 * q^74 - 800 * q^75 + 861 * q^76 + 1275 * q^77 + 16 * q^78 - 846 * q^79 - 615 * q^80 - 359 * q^81 + 387 * q^82 + 1352 * q^83 - 1400 * q^84 - 465 * q^85 + 80 * q^86 - 48 * q^87 - 765 * q^88 + 1242 * q^89 + 555 * q^90 - 50 * q^91 + 1043 * q^92 - 80 * q^93 - 266 * q^94 + 1845 * q^95 + 1288 * q^96 + 632 * q^97 - 282 * q^98 - 1887 * 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

−1.00000

−8.00000

−7.00000

−15.0000

8.00000

−25.0000

15.0000

37.0000

15.0000

Atkin-Lehner signs

$p$	Sign
$127$	$+1$

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	127.4.a.a	✓	1
3.b	odd	2	1		1143.4.a.a		1
4.b	odd	2	1		2032.4.a.b		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
127.4.a.a	✓	1	1.a	even	1	1	trivial
1143.4.a.a		1	3.b	odd	2	1
2032.4.a.b		1	4.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{2} + 1$ acting on $S_{4}^{\mathrm{new}}(\Gamma_0(127))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 1$
$3$	$T + 8$
$5$	$T + 15$
$7$	$T + 25$
$11$	$T + 51$