Newform orbit 1452.3.e.d

• Label: 1452.3.e.d
• Level: $1452$
• Weight: $3$
• Character orbit: 1452.e
• Analytic conductor: $39.564$
• Analytic rank: $0$
• Dimension: $2$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1452.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(39.5641343851\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{-11}) \)
Defining polynomial:	\( x^{2} - x + 3 \)
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 132)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{-11})\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	q + (-b + 3) * q^3 + (-2*b + 1) * q^5 - 2 * q^7 + (-5*b + 6) * q^9 + (-5*b - 3) * q^15 + (-4*b + 2) * q^17 - 4 * q^19 + (2*b - 6) * q^21 + (2*b - 1) * q^23 + 14 * q^25 + (-16*b + 3) * q^27 + (-24*b + 12) * q^29 + 9 * q^31 + (4*b - 2) * q^35 - 51 * q^37 + (-48*b + 24) * q^41 - 22 * q^43 + (-7*b - 24) * q^45 + (24*b - 12) * q^47 - 45 * q^49 + (-10*b - 6) * q^51 + (40*b - 20) * q^53 + (4*b - 12) * q^57 + (-42*b + 21) * q^59 + 80 * q^61 + (10*b - 12) * q^63 + q^67 + (5*b + 3) * q^69 + (-30*b + 15) * q^71 - 108 * q^73 + (-14*b + 42) * q^75 - 122 * q^79 + (-35*b - 39) * q^81 + (52*b - 26) * q^83 - 22 * q^85 + (-60*b - 36) * q^87 + (-58*b + 29) * q^89 + (-9*b + 27) * q^93 + (8*b - 4) * q^95 + 79 * q^97
\(\operatorname{Tr}(f)(q)\)	\(=\)	2 * q + 5 * q^3 - 4 * q^7 + 7 * q^9 - 11 * q^15 - 8 * q^19 - 10 * q^21 + 28 * q^25 - 10 * q^27 + 18 * q^31 - 102 * q^37 - 44 * q^43 - 55 * q^45 - 90 * q^49 - 22 * q^51 - 20 * q^57 + 160 * q^61 - 14 * q^63 + 2 * q^67 + 11 * q^69 - 216 * q^73 + 70 * q^75 - 244 * q^79 - 113 * q^81 - 44 * q^85 - 132 * q^87 + 45 * q^93 + 158 * q^97

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1452\mathbb{Z}\right)^\times\).

\(n\)	\(485\)	\(727\)	\(1333\)
\(\chi(n)\)	\(-1\)	\(1\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

485.1

0.500000	+	1.65831i
0.500000	−	1.65831i

0

2.50000

−

1.65831i

0

−

3.31662i

0

−2.00000

0

3.50000

−

8.29156i

0

485.2

0

2.50000

+

1.65831i

0

3.31662i

0

−2.00000

0

3.50000

+

8.29156i

0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1452.3.e.d		2
3.b	odd	2	1	inner	1452.3.e.d		2
11.b	odd	2	1		132.3.e.a	✓	2
33.d	even	2	1		132.3.e.a	✓	2
44.c	even	2	1		528.3.i.b		2
132.d	odd	2	1		528.3.i.b		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
132.3.e.a	✓	2	11.b	odd	2	1
132.3.e.a	✓	2	33.d	even	2	1
528.3.i.b		2	44.c	even	2	1
528.3.i.b		2	132.d	odd	2	1
1452.3.e.d		2	1.a	even	1	1	trivial
1452.3.e.d		2	3.b	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(1452, [\chi])\):

\( T_{5}^{2} + 11 \)

\( T_{7} + 2 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} - 5T + 9 \)
$5$	\( T^{2} + 11 \)
$7$	\( (T + 2)^{2} \)
$11$	\( T^{2} \)