# Properties

 Label 2100.2.s.c Level 2100 Weight 2 Character orbit 2100.s Analytic conductor 16.769 Analytic rank 0 Dimension 32 CM no Inner twists 8

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2100.s (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$16.7685844245$$ Analytic rank: $$0$$ Dimension: $$32$$ Relative dimension: $$16$$ over $$\Q(i)$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## $q$-expansion

The dimension is sufficiently large that we do not compute an algebraic $$q$$-expansion, but we have computed the trace expansion.

 $$\operatorname{Tr}(f)(q) =$$ $$32q + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$32q - 8q^{21} + 48q^{31} - 32q^{51} + 16q^{61} + 64q^{81} + 32q^{91} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1457.1 0 −1.73156 0.0412661i 0 0 0 0.707107 + 0.707107i 0 2.99659 + 0.142909i 0
1457.2 0 −1.69214 + 0.369667i 0 0 0 0.707107 + 0.707107i 0 2.72669 1.25106i 0
1457.3 0 −1.63431 + 0.573626i 0 0 0 −0.707107 0.707107i 0 2.34191 1.87496i 0
1457.4 0 −1.28800 1.15804i 0 0 0 −0.707107 0.707107i 0 0.317883 + 2.98311i 0
1457.5 0 −1.15804 1.28800i 0 0 0 0.707107 + 0.707107i 0 −0.317883 + 2.98311i 0
1457.6 0 −0.573626 + 1.63431i 0 0 0 −0.707107 0.707107i 0 −2.34191 1.87496i 0
1457.7 0 −0.369667 + 1.69214i 0 0 0 0.707107 + 0.707107i 0 −2.72669 1.25106i 0
1457.8 0 −0.0412661 1.73156i 0 0 0 −0.707107 0.707107i 0 −2.99659 + 0.142909i 0
1457.9 0 0.0412661 + 1.73156i 0 0 0 0.707107 + 0.707107i 0 −2.99659 + 0.142909i 0
1457.10 0 0.369667 1.69214i 0 0 0 −0.707107 0.707107i 0 −2.72669 1.25106i 0
1457.11 0 0.573626 1.63431i 0 0 0 0.707107 + 0.707107i 0 −2.34191 1.87496i 0
1457.12 0 1.15804 + 1.28800i 0 0 0 −0.707107 0.707107i 0 −0.317883 + 2.98311i 0
1457.13 0 1.28800 + 1.15804i 0 0 0 0.707107 + 0.707107i 0 0.317883 + 2.98311i 0
1457.14 0 1.63431 0.573626i 0 0 0 0.707107 + 0.707107i 0 2.34191 1.87496i 0
1457.15 0 1.69214 0.369667i 0 0 0 −0.707107 0.707107i 0 2.72669 1.25106i 0
1457.16 0 1.73156 + 0.0412661i 0 0 0 −0.707107 0.707107i 0 2.99659 + 0.142909i 0
1793.1 0 −1.73156 + 0.0412661i 0 0 0 0.707107 0.707107i 0 2.99659 0.142909i 0
1793.2 0 −1.69214 0.369667i 0 0 0 0.707107 0.707107i 0 2.72669 + 1.25106i 0
1793.3 0 −1.63431 0.573626i 0 0 0 −0.707107 + 0.707107i 0 2.34191 + 1.87496i 0
1793.4 0 −1.28800 + 1.15804i 0 0 0 −0.707107 + 0.707107i 0 0.317883 2.98311i 0
See all 32 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1793.16 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.b even 2 1 inner
5.c odd 4 2 inner
15.d odd 2 1 inner
15.e even 4 2 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2100.2.s.c 32
3.b odd 2 1 inner 2100.2.s.c 32
5.b even 2 1 inner 2100.2.s.c 32
5.c odd 4 2 inner 2100.2.s.c 32
15.d odd 2 1 inner 2100.2.s.c 32
15.e even 4 2 inner 2100.2.s.c 32

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2100.2.s.c 32 1.a even 1 1 trivial
2100.2.s.c 32 3.b odd 2 1 inner
2100.2.s.c 32 5.b even 2 1 inner
2100.2.s.c 32 5.c odd 4 2 inner
2100.2.s.c 32 15.d odd 2 1 inner
2100.2.s.c 32 15.e even 4 2 inner

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{11}^{8} + 60 T_{11}^{6} + 962 T_{11}^{4} + 4452 T_{11}^{2} + 6253$$ acting on $$S_{2}^{\mathrm{new}}(2100, [\chi])$$.

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database