Properties

Label 2695.1.q.c
Level $2695$
Weight $1$
Character orbit 2695.q
Analytic conductor $1.345$
Analytic rank $0$
Dimension $2$
Projective image $D_{2}$
CM/RM discs -11, -55, 5
Inner twists $8$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2695.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.34498020905\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
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: $C_3\times D_4$
Artin field: Galois closure of \(\mathbb{Q}[x]/(x^{12} - \cdots)\)

$q$-expansion

The \(q\)-expansion and trace form are shown below.

\(f(q)\) \(=\) \( q - \zeta_{6}^{2} q^{4} + \zeta_{6} q^{5} - \zeta_{6} q^{9} +O(q^{10}) \) Copy content Toggle raw display \( q - \zeta_{6}^{2} q^{4} + \zeta_{6} q^{5} - \zeta_{6} q^{9} - \zeta_{6}^{2} q^{11} - \zeta_{6} q^{16} + q^{20} + \zeta_{6}^{2} q^{25} - \zeta_{6}^{2} q^{31} - q^{36} - \zeta_{6} q^{44} - \zeta_{6}^{2} q^{45} + q^{55} + \zeta_{6}^{2} q^{59} - q^{64} + q^{71} - \zeta_{6}^{2} q^{80} + \zeta_{6}^{2} q^{81} + \zeta_{6} q^{89} - q^{99} +O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{4} + q^{5} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{4} + q^{5} - q^{9} + q^{11} - q^{16} + 2 q^{20} - q^{25} + 2 q^{31} - 2 q^{36} - q^{44} + q^{45} + 2 q^{55} - 2 q^{59} - 2 q^{64} + 4 q^{71} + q^{80} - q^{81} + 2 q^{89} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2695\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1816\) \(2157\)
\(\chi(n)\) \(-1\) \(-\zeta_{6}\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2419.1
0.500000 + 0.866025i
0.500000 0.866025i
0 0 0.500000 0.866025i 0.500000 + 0.866025i 0 0 0 −0.500000 0.866025i 0
2529.1 0 0 0.500000 + 0.866025i 0.500000 0.866025i 0 0 0 −0.500000 + 0.866025i 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 \(\Q(\sqrt{-55}) \)
7.c even 3 1 inner
35.j even 6 1 inner
77.h odd 6 1 inner
385.q odd 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2695.1.q.c 2
5.b even 2 1 RM 2695.1.q.c 2
7.b odd 2 1 2695.1.q.b 2
7.c even 3 1 55.1.d.a 1
7.c even 3 1 inner 2695.1.q.c 2
7.d odd 6 1 2695.1.g.c 1
7.d odd 6 1 2695.1.q.b 2
11.b odd 2 1 CM 2695.1.q.c 2
21.h odd 6 1 495.1.h.a 1
28.g odd 6 1 880.1.i.a 1
35.c odd 2 1 2695.1.q.b 2
35.i odd 6 1 2695.1.g.c 1
35.i odd 6 1 2695.1.q.b 2
35.j even 6 1 55.1.d.a 1
35.j even 6 1 inner 2695.1.q.c 2
35.l odd 12 2 275.1.c.a 1
55.d odd 2 1 CM 2695.1.q.c 2
56.k odd 6 1 3520.1.i.a 1
56.p even 6 1 3520.1.i.b 1
77.b even 2 1 2695.1.q.b 2
77.h odd 6 1 55.1.d.a 1
77.h odd 6 1 inner 2695.1.q.c 2
77.i even 6 1 2695.1.g.c 1
77.i even 6 1 2695.1.q.b 2
77.m even 15 4 605.1.h.a 4
77.o odd 30 4 605.1.h.a 4
105.o odd 6 1 495.1.h.a 1
105.x even 12 2 2475.1.b.a 1
140.p odd 6 1 880.1.i.a 1
231.l even 6 1 495.1.h.a 1
280.bf even 6 1 3520.1.i.b 1
280.bi odd 6 1 3520.1.i.a 1
308.n even 6 1 880.1.i.a 1
385.h even 2 1 2695.1.q.b 2
385.o even 6 1 2695.1.g.c 1
385.o even 6 1 2695.1.q.b 2
385.q odd 6 1 55.1.d.a 1
385.q odd 6 1 inner 2695.1.q.c 2
385.bc even 12 2 275.1.c.a 1
385.bm even 30 4 605.1.h.a 4
385.bp odd 30 4 605.1.h.a 4
385.bt odd 60 8 3025.1.x.a 4
385.bv even 60 8 3025.1.x.a 4
616.y even 6 1 3520.1.i.a 1
616.bg odd 6 1 3520.1.i.b 1
1155.bo even 6 1 495.1.h.a 1
1155.cg odd 12 2 2475.1.b.a 1
1540.be even 6 1 880.1.i.a 1
3080.bz odd 6 1 3520.1.i.b 1
3080.cq even 6 1 3520.1.i.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
55.1.d.a 1 7.c even 3 1
55.1.d.a 1 35.j even 6 1
55.1.d.a 1 77.h odd 6 1
55.1.d.a 1 385.q odd 6 1
275.1.c.a 1 35.l odd 12 2
275.1.c.a 1 385.bc even 12 2
495.1.h.a 1 21.h odd 6 1
495.1.h.a 1 105.o odd 6 1
495.1.h.a 1 231.l even 6 1
495.1.h.a 1 1155.bo even 6 1
605.1.h.a 4 77.m even 15 4
605.1.h.a 4 77.o odd 30 4
605.1.h.a 4 385.bm even 30 4
605.1.h.a 4 385.bp odd 30 4
880.1.i.a 1 28.g odd 6 1
880.1.i.a 1 140.p odd 6 1
880.1.i.a 1 308.n even 6 1
880.1.i.a 1 1540.be even 6 1
2475.1.b.a 1 105.x even 12 2
2475.1.b.a 1 1155.cg odd 12 2
2695.1.g.c 1 7.d odd 6 1
2695.1.g.c 1 35.i odd 6 1
2695.1.g.c 1 77.i even 6 1
2695.1.g.c 1 385.o even 6 1
2695.1.q.b 2 7.b odd 2 1
2695.1.q.b 2 7.d odd 6 1
2695.1.q.b 2 35.c odd 2 1
2695.1.q.b 2 35.i odd 6 1
2695.1.q.b 2 77.b even 2 1
2695.1.q.b 2 77.i even 6 1
2695.1.q.b 2 385.h even 2 1
2695.1.q.b 2 385.o even 6 1
2695.1.q.c 2 1.a even 1 1 trivial
2695.1.q.c 2 5.b even 2 1 RM
2695.1.q.c 2 7.c even 3 1 inner
2695.1.q.c 2 11.b odd 2 1 CM
2695.1.q.c 2 35.j even 6 1 inner
2695.1.q.c 2 55.d odd 2 1 CM
2695.1.q.c 2 77.h odd 6 1 inner
2695.1.q.c 2 385.q odd 6 1 inner
3025.1.x.a 4 385.bt odd 60 8
3025.1.x.a 4 385.bv even 60 8
3520.1.i.a 1 56.k odd 6 1
3520.1.i.a 1 280.bi odd 6 1
3520.1.i.a 1 616.y even 6 1
3520.1.i.a 1 3080.cq even 6 1
3520.1.i.b 1 56.p even 6 1
3520.1.i.b 1 280.bf even 6 1
3520.1.i.b 1 616.bg odd 6 1
3520.1.i.b 1 3080.bz odd 6 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(2695, [\chi])\):

\( T_{2} \) Copy content Toggle raw display
\( T_{3} \) Copy content Toggle raw display
\( T_{31}^{2} - 2T_{31} + 4 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T^{2} \) Copy content Toggle raw display
$3$ \( T^{2} \) Copy content Toggle raw display
$5$ \( T^{2} - T + 1 \) Copy content Toggle raw display
$7$ \( T^{2} \) Copy content Toggle raw display
$11$ \( T^{2} - T + 1 \) Copy content Toggle raw display
$13$ \( T^{2} \) Copy content Toggle raw display
$17$ \( T^{2} \) Copy content Toggle raw display
$19$ \( T^{2} \) Copy content Toggle raw display
$23$ \( T^{2} \) Copy content Toggle raw display
$29$ \( T^{2} \) Copy content Toggle raw display
$31$ \( T^{2} - 2T + 4 \) Copy content Toggle raw display
$37$ \( T^{2} \) Copy content Toggle raw display
$41$ \( T^{2} \) Copy content Toggle raw display
$43$ \( T^{2} \) Copy content Toggle raw display
$47$ \( T^{2} \) Copy content Toggle raw display
$53$ \( T^{2} \) Copy content Toggle raw display
$59$ \( T^{2} + 2T + 4 \) Copy content Toggle raw display
$61$ \( T^{2} \) Copy content Toggle raw display
$67$ \( T^{2} \) Copy content Toggle raw display
$71$ \( (T - 2)^{2} \) Copy content Toggle raw display
$73$ \( T^{2} \) Copy content Toggle raw display
$79$ \( T^{2} \) Copy content Toggle raw display
$83$ \( T^{2} \) Copy content Toggle raw display
$89$ \( T^{2} - 2T + 4 \) Copy content Toggle raw display
$97$ \( T^{2} \) Copy content Toggle raw display
show more
show less