Newform orbit 275.2.a.c

• Label: 275.2.a.c
• Level: $275$
• Weight: $2$
• Character orbit: 275.a
• Self dual: yes
• Analytic conductor: $2.196$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(2.19588605559\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{2}) \)
Defining polynomial:	\( x^{2} - 2 \)
Coefficient ring:	\(\Z[a_1, a_2]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

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

\(f(q)\)	\(=\)	\( q + (\beta - 1) q^{2} - 2 \beta q^{3} + ( - 2 \beta + 1) q^{4} + (2 \beta - 4) q^{6} + 2 q^{7} + (\beta - 3) q^{8} + 5 q^{9} +O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 8 q^{6} + 4 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) \)

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

−1.41421
1.41421

−2.41421

2.82843

3.82843

0

−6.82843

2.00000

−4.41421

5.00000

0

1.2

0.414214

−2.82843

−1.82843

0

−1.17157

2.00000

−1.58579

5.00000

0

Atkin-Lehner signs

\( p \)	Sign
\(5\)	\(1\)
\(11\)	\(-1\)

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	275.2.a.c		2
3.b	odd	2	1		2475.2.a.x		2
4.b	odd	2	1		4400.2.a.bn		2
5.b	even	2	1		55.2.a.b	✓	2
5.c	odd	4	2		275.2.b.d		4
11.b	odd	2	1		3025.2.a.o		2
15.d	odd	2	1		495.2.a.b		2
15.e	even	4	2		2475.2.c.l		4
20.d	odd	2	1		880.2.a.m		2
20.e	even	4	2		4400.2.b.q		4
35.c	odd	2	1		2695.2.a.f		2
40.e	odd	2	1		3520.2.a.bo		2
40.f	even	2	1		3520.2.a.bn		2
55.d	odd	2	1		605.2.a.d		2
55.h	odd	10	4		605.2.g.l		8
55.j	even	10	4		605.2.g.f		8
60.h	even	2	1		7920.2.a.ch		2
65.d	even	2	1		9295.2.a.g		2
165.d	even	2	1		5445.2.a.y		2
220.g	even	2	1		9680.2.a.bn		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
55.2.a.b	✓	2	5.b	even	2	1
275.2.a.c		2	1.a	even	1	1	trivial
275.2.b.d		4	5.c	odd	4	2
495.2.a.b		2	15.d	odd	2	1
605.2.a.d		2	55.d	odd	2	1
605.2.g.f		8	55.j	even	10	4
605.2.g.l		8	55.h	odd	10	4
880.2.a.m		2	20.d	odd	2	1
2475.2.a.x		2	3.b	odd	2	1
2475.2.c.l		4	15.e	even	4	2
2695.2.a.f		2	35.c	odd	2	1
3025.2.a.o		2	11.b	odd	2	1
3520.2.a.bn		2	40.f	even	2	1
3520.2.a.bo		2	40.e	odd	2	1
4400.2.a.bn		2	4.b	odd	2	1
4400.2.b.q		4	20.e	even	4	2
5445.2.a.y		2	165.d	even	2	1
7920.2.a.ch		2	60.h	even	2	1
9295.2.a.g		2	65.d	even	2	1
9680.2.a.bn		2	220.g	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{2} + 2T_{2} - 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(275))\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} + 2T - 1 \)
$3$	\( T^{2} - 8 \)
$5$	\( T^{2} \)
$7$	\( (T - 2)^{2} \)
$11$	\( (T - 1)^{2} \)