Properties

Label 275.1.c.a
Level $275$
Weight $1$
Character orbit 275.c
Self dual yes
Analytic conductor $0.137$
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: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 275.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.137242878474\)
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 4.2.1375.1

$q$-expansion

\(f(q)\) \(=\) \( q + q^{4} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{4} - q^{9} - q^{11} + q^{16} - 2 q^{31} - q^{36} - q^{44} + q^{49} - 2 q^{59} + q^{64} + 2 q^{71} + q^{81} + 2 q^{89} + q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/275\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\)
\(\chi(n)\) \(-1\) \(1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
76.1
0
0 0 1.00000 0 0 0 0 −1.00000 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 275.1.c.a 1
3.b odd 2 1 2475.1.b.a 1
5.b even 2 1 RM 275.1.c.a 1
5.c odd 4 2 55.1.d.a 1
11.b odd 2 1 CM 275.1.c.a 1
11.c even 5 4 3025.1.x.a 4
11.d odd 10 4 3025.1.x.a 4
15.d odd 2 1 2475.1.b.a 1
15.e even 4 2 495.1.h.a 1
20.e even 4 2 880.1.i.a 1
33.d even 2 1 2475.1.b.a 1
35.f even 4 2 2695.1.g.c 1
35.k even 12 4 2695.1.q.b 2
35.l odd 12 4 2695.1.q.c 2
40.i odd 4 2 3520.1.i.b 1
40.k even 4 2 3520.1.i.a 1
55.d odd 2 1 CM 275.1.c.a 1
55.e even 4 2 55.1.d.a 1
55.h odd 10 4 3025.1.x.a 4
55.j even 10 4 3025.1.x.a 4
55.k odd 20 8 605.1.h.a 4
55.l even 20 8 605.1.h.a 4
165.d even 2 1 2475.1.b.a 1
165.l odd 4 2 495.1.h.a 1
220.i odd 4 2 880.1.i.a 1
385.l odd 4 2 2695.1.g.c 1
385.bc even 12 4 2695.1.q.c 2
385.bf odd 12 4 2695.1.q.b 2
440.t even 4 2 3520.1.i.b 1
440.w odd 4 2 3520.1.i.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
55.1.d.a 1 5.c odd 4 2
55.1.d.a 1 55.e even 4 2
275.1.c.a 1 1.a even 1 1 trivial
275.1.c.a 1 5.b even 2 1 RM
275.1.c.a 1 11.b odd 2 1 CM
275.1.c.a 1 55.d odd 2 1 CM
495.1.h.a 1 15.e even 4 2
495.1.h.a 1 165.l odd 4 2
605.1.h.a 4 55.k odd 20 8
605.1.h.a 4 55.l even 20 8
880.1.i.a 1 20.e even 4 2
880.1.i.a 1 220.i odd 4 2
2475.1.b.a 1 3.b odd 2 1
2475.1.b.a 1 15.d odd 2 1
2475.1.b.a 1 33.d even 2 1
2475.1.b.a 1 165.d even 2 1
2695.1.g.c 1 35.f even 4 2
2695.1.g.c 1 385.l odd 4 2
2695.1.q.b 2 35.k even 12 4
2695.1.q.b 2 385.bf odd 12 4
2695.1.q.c 2 35.l odd 12 4
2695.1.q.c 2 385.bc even 12 4
3025.1.x.a 4 11.c even 5 4
3025.1.x.a 4 11.d odd 10 4
3025.1.x.a 4 55.h odd 10 4
3025.1.x.a 4 55.j even 10 4
3520.1.i.a 1 40.k even 4 2
3520.1.i.a 1 440.w odd 4 2
3520.1.i.b 1 40.i odd 4 2
3520.1.i.b 1 440.t even 4 2

Hecke kernels

This newform subspace is the entire newspace \(S_{1}^{\mathrm{new}}(275, [\chi])\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T \) 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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