# Properties

 Label 2835.1.e.c Level $2835$ Weight $1$ Character orbit 2835.e Self dual yes Analytic conductor $1.415$ Analytic rank $0$ Dimension $1$ Projective image $D_{3}$ CM discriminant -35 Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2835 = 3^{4} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2835.e (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: yes Analytic conductor: $$1.41484931081$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 315) Projective image $$D_{3}$$ Projective field Galois closure of 3.1.2835.1 Artin image $D_6$ Artin field Galois closure of 6.0.120558375.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{4} + q^{5} - q^{7} + O(q^{10})$$ $$q + q^{4} + q^{5} - q^{7} + q^{11} + q^{13} + q^{16} - q^{17} + q^{20} + q^{25} - q^{28} - 2q^{29} - q^{35} + q^{44} - q^{47} + q^{49} + q^{52} + q^{55} + q^{64} + q^{65} - q^{68} + q^{71} + q^{73} - q^{77} - q^{79} + q^{80} - q^{83} - q^{85} - q^{91} + q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2835\mathbb{Z}\right)^\times$$.

 $$n$$ $$1541$$ $$1702$$ $$2026$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$

## 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 $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
244.1
 0
0 0 1.00000 1.00000 0 −1.00000 0 0 0
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
35.c odd 2 1 CM by $$\Q(\sqrt{-35})$$

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2835.1.e.c 1
3.b odd 2 1 2835.1.e.a 1
5.b even 2 1 2835.1.e.b 1
7.b odd 2 1 2835.1.e.b 1
9.c even 3 2 945.1.bg.a 2
9.d odd 6 2 315.1.bg.a 2
15.d odd 2 1 2835.1.e.d 1
21.c even 2 1 2835.1.e.d 1
35.c odd 2 1 CM 2835.1.e.c 1
45.h odd 6 2 315.1.bg.b yes 2
45.j even 6 2 945.1.bg.b 2
45.l even 12 4 1575.1.y.a 4
63.i even 6 2 2205.1.q.a 2
63.j odd 6 2 2205.1.q.b 2
63.l odd 6 2 945.1.bg.b 2
63.n odd 6 2 2205.1.bn.b 2
63.o even 6 2 315.1.bg.b yes 2
63.s even 6 2 2205.1.bn.a 2
105.g even 2 1 2835.1.e.a 1
315.u even 6 2 2205.1.bn.b 2
315.v odd 6 2 2205.1.bn.a 2
315.z even 6 2 315.1.bg.a 2
315.bg odd 6 2 945.1.bg.a 2
315.bq even 6 2 2205.1.q.b 2
315.br odd 6 2 2205.1.q.a 2
315.cf odd 12 4 1575.1.y.a 4

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
315.1.bg.a 2 9.d odd 6 2
315.1.bg.a 2 315.z even 6 2
315.1.bg.b yes 2 45.h odd 6 2
315.1.bg.b yes 2 63.o even 6 2
945.1.bg.a 2 9.c even 3 2
945.1.bg.a 2 315.bg odd 6 2
945.1.bg.b 2 45.j even 6 2
945.1.bg.b 2 63.l odd 6 2
1575.1.y.a 4 45.l even 12 4
1575.1.y.a 4 315.cf odd 12 4
2205.1.q.a 2 63.i even 6 2
2205.1.q.a 2 315.br odd 6 2
2205.1.q.b 2 63.j odd 6 2
2205.1.q.b 2 315.bq even 6 2
2205.1.bn.a 2 63.s even 6 2
2205.1.bn.a 2 315.v odd 6 2
2205.1.bn.b 2 63.n odd 6 2
2205.1.bn.b 2 315.u even 6 2
2835.1.e.a 1 3.b odd 2 1
2835.1.e.a 1 105.g even 2 1
2835.1.e.b 1 5.b even 2 1
2835.1.e.b 1 7.b odd 2 1
2835.1.e.c 1 1.a even 1 1 trivial
2835.1.e.c 1 35.c odd 2 1 CM
2835.1.e.d 1 15.d odd 2 1
2835.1.e.d 1 21.c even 2 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{1}^{\mathrm{new}}(2835, [\chi])$$:

 $$T_{11} - 1$$ $$T_{13} - 1$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$( 1 - T )( 1 + T )$$
$3$ 1
$5$ $$1 - T$$
$7$ $$1 + T$$
$11$ $$1 - T + T^{2}$$
$13$ $$1 - T + T^{2}$$
$17$ $$1 + T + T^{2}$$
$19$ $$( 1 - T )( 1 + T )$$
$23$ $$( 1 - T )( 1 + T )$$
$29$ $$( 1 + T )^{2}$$
$31$ $$( 1 - T )( 1 + T )$$
$37$ $$( 1 - T )( 1 + T )$$
$41$ $$( 1 - T )( 1 + T )$$
$43$ $$( 1 - T )( 1 + T )$$
$47$ $$1 + T + T^{2}$$
$53$ $$( 1 - T )( 1 + T )$$
$59$ $$( 1 - T )( 1 + T )$$
$61$ $$( 1 - T )( 1 + T )$$
$67$ $$( 1 - T )( 1 + T )$$
$71$ $$1 - T + T^{2}$$
$73$ $$1 - T + T^{2}$$
$79$ $$1 + T + T^{2}$$
$83$ $$1 + T + T^{2}$$
$89$ $$( 1 - T )( 1 + T )$$
$97$ $$1 - T + T^{2}$$