Properties

Label 495.1.h.a
Level $495$
Weight $1$
Character orbit 495.h
Self dual yes
Analytic conductor $0.247$
Analytic rank $0$
Dimension $1$
Projective image $D_{2}$
CM/RM discs -11, -55, 5
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 495.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.247037181253\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Projective image: \(D_{2}\)
Projective field: Galois closure of \(\Q(\sqrt{5}, \sqrt{-11})\)
Artin image: $D_4$
Artin field: Galois closure of 4.2.2475.1

$q$-expansion

\(f(q)\) \(=\) \( q - q^{4} + q^{5}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{4} + q^{5} + q^{11} + q^{16} - q^{20} + q^{25} - 2 q^{31} - q^{44} - q^{49} + q^{55} - 2 q^{59} - q^{64} - 2 q^{71} + q^{80} + 2 q^{89}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(397\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
109.1
0
0 0 −1.00000 1.00000 0 0 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 RM by \(\Q(\sqrt{5}) \)
11.b odd 2 1 CM by \(\Q(\sqrt{-11}) \)
55.d odd 2 1 CM by \(\Q(\sqrt{-55}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 495.1.h.a 1
3.b odd 2 1 55.1.d.a 1
5.b even 2 1 RM 495.1.h.a 1
5.c odd 4 2 2475.1.b.a 1
11.b odd 2 1 CM 495.1.h.a 1
12.b even 2 1 880.1.i.a 1
15.d odd 2 1 55.1.d.a 1
15.e even 4 2 275.1.c.a 1
21.c even 2 1 2695.1.g.c 1
21.g even 6 2 2695.1.q.b 2
21.h odd 6 2 2695.1.q.c 2
24.f even 2 1 3520.1.i.a 1
24.h odd 2 1 3520.1.i.b 1
33.d even 2 1 55.1.d.a 1
33.f even 10 4 605.1.h.a 4
33.h odd 10 4 605.1.h.a 4
55.d odd 2 1 CM 495.1.h.a 1
55.e even 4 2 2475.1.b.a 1
60.h even 2 1 880.1.i.a 1
105.g even 2 1 2695.1.g.c 1
105.o odd 6 2 2695.1.q.c 2
105.p even 6 2 2695.1.q.b 2
120.i odd 2 1 3520.1.i.b 1
120.m even 2 1 3520.1.i.a 1
132.d odd 2 1 880.1.i.a 1
165.d even 2 1 55.1.d.a 1
165.l odd 4 2 275.1.c.a 1
165.o odd 10 4 605.1.h.a 4
165.r even 10 4 605.1.h.a 4
165.u odd 20 8 3025.1.x.a 4
165.v even 20 8 3025.1.x.a 4
231.h odd 2 1 2695.1.g.c 1
231.k odd 6 2 2695.1.q.b 2
231.l even 6 2 2695.1.q.c 2
264.m even 2 1 3520.1.i.b 1
264.p odd 2 1 3520.1.i.a 1
660.g odd 2 1 880.1.i.a 1
1155.e odd 2 1 2695.1.g.c 1
1155.bh odd 6 2 2695.1.q.b 2
1155.bo even 6 2 2695.1.q.c 2
1320.b odd 2 1 3520.1.i.a 1
1320.u even 2 1 3520.1.i.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
55.1.d.a 1 3.b odd 2 1
55.1.d.a 1 15.d odd 2 1
55.1.d.a 1 33.d even 2 1
55.1.d.a 1 165.d even 2 1
275.1.c.a 1 15.e even 4 2
275.1.c.a 1 165.l odd 4 2
495.1.h.a 1 1.a even 1 1 trivial
495.1.h.a 1 5.b even 2 1 RM
495.1.h.a 1 11.b odd 2 1 CM
495.1.h.a 1 55.d odd 2 1 CM
605.1.h.a 4 33.f even 10 4
605.1.h.a 4 33.h odd 10 4
605.1.h.a 4 165.o odd 10 4
605.1.h.a 4 165.r even 10 4
880.1.i.a 1 12.b even 2 1
880.1.i.a 1 60.h even 2 1
880.1.i.a 1 132.d odd 2 1
880.1.i.a 1 660.g odd 2 1
2475.1.b.a 1 5.c odd 4 2
2475.1.b.a 1 55.e even 4 2
2695.1.g.c 1 21.c even 2 1
2695.1.g.c 1 105.g even 2 1
2695.1.g.c 1 231.h odd 2 1
2695.1.g.c 1 1155.e odd 2 1
2695.1.q.b 2 21.g even 6 2
2695.1.q.b 2 105.p even 6 2
2695.1.q.b 2 231.k odd 6 2
2695.1.q.b 2 1155.bh odd 6 2
2695.1.q.c 2 21.h odd 6 2
2695.1.q.c 2 105.o odd 6 2
2695.1.q.c 2 231.l even 6 2
2695.1.q.c 2 1155.bo even 6 2
3025.1.x.a 4 165.u odd 20 8
3025.1.x.a 4 165.v even 20 8
3520.1.i.a 1 24.f even 2 1
3520.1.i.a 1 120.m even 2 1
3520.1.i.a 1 264.p odd 2 1
3520.1.i.a 1 1320.b odd 2 1
3520.1.i.b 1 24.h odd 2 1
3520.1.i.b 1 120.i odd 2 1
3520.1.i.b 1 264.m even 2 1
3520.1.i.b 1 1320.u even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(495, [\chi])\):

\( T_{2} \) Copy content Toggle raw display
\( T_{89} - 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T - 1 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T - 1 \) Copy content Toggle raw display
$13$ \( T \) Copy content Toggle raw display
$17$ \( T \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T \) Copy content Toggle raw display
$29$ \( T \) Copy content Toggle raw display
$31$ \( T + 2 \) Copy content Toggle raw display
$37$ \( T \) Copy content Toggle raw display
$41$ \( T \) Copy content Toggle raw display
$43$ \( T \) Copy content Toggle raw display
$47$ \( T \) Copy content Toggle raw display
$53$ \( T \) Copy content Toggle raw display
$59$ \( T + 2 \) Copy content Toggle raw display
$61$ \( T \) Copy content Toggle raw display
$67$ \( T \) Copy content Toggle raw display
$71$ \( T + 2 \) Copy content Toggle raw display
$73$ \( T \) Copy content Toggle raw display
$79$ \( T \) Copy content Toggle raw display
$83$ \( T \) Copy content Toggle raw display
$89$ \( T - 2 \) Copy content Toggle raw display
$97$ \( T \) Copy content Toggle raw display
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