# Properties

 Label 2100.2.bo.i Level 2100 Weight 2 Character orbit 2100.bo 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.bo (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$16.7685844245$$ Analytic rank: $$0$$ Dimension: $$32$$ Relative dimension: $$16$$ over $$\Q(\zeta_{6})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## $q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$32q + 18q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$32q + 18q^{9} + 36q^{19} - 22q^{21} - 36q^{31} - 24q^{39} + 36q^{49} - 2q^{51} + 72q^{61} + 14q^{81} + 40q^{91} + 60q^{99} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1349.1 0 −1.68420 + 0.404332i 0 0 0 2.10133 1.60761i 0 2.67303 1.36195i 0
1349.2 0 −1.68089 0.417865i 0 0 0 2.33003 1.25338i 0 2.65078 + 1.40477i 0
1349.3 0 −1.56849 + 0.734734i 0 0 0 0.156656 + 2.64111i 0 1.92033 2.30485i 0
1349.4 0 −1.56253 0.747325i 0 0 0 −2.52603 0.786875i 0 1.88301 + 2.33544i 0
1349.5 0 −1.42054 + 0.990987i 0 0 0 −0.156656 2.64111i 0 1.03589 2.81548i 0
1349.6 0 −1.19226 + 1.25639i 0 0 0 −2.10133 + 1.60761i 0 −0.157032 2.99589i 0
1349.7 0 −0.478563 + 1.66463i 0 0 0 −2.33003 + 1.25338i 0 −2.54196 1.59326i 0
1349.8 0 −0.134063 + 1.72685i 0 0 0 2.52603 + 0.786875i 0 −2.96405 0.463016i 0
1349.9 0 0.134063 1.72685i 0 0 0 −2.52603 0.786875i 0 −2.96405 0.463016i 0
1349.10 0 0.478563 1.66463i 0 0 0 2.33003 1.25338i 0 −2.54196 1.59326i 0
1349.11 0 1.19226 1.25639i 0 0 0 2.10133 1.60761i 0 −0.157032 2.99589i 0
1349.12 0 1.42054 0.990987i 0 0 0 0.156656 + 2.64111i 0 1.03589 2.81548i 0
1349.13 0 1.56253 + 0.747325i 0 0 0 2.52603 + 0.786875i 0 1.88301 + 2.33544i 0
1349.14 0 1.56849 0.734734i 0 0 0 −0.156656 2.64111i 0 1.92033 2.30485i 0
1349.15 0 1.68089 + 0.417865i 0 0 0 −2.33003 + 1.25338i 0 2.65078 + 1.40477i 0
1349.16 0 1.68420 0.404332i 0 0 0 −2.10133 + 1.60761i 0 2.67303 1.36195i 0
1949.1 0 −1.68420 0.404332i 0 0 0 2.10133 + 1.60761i 0 2.67303 + 1.36195i 0
1949.2 0 −1.68089 + 0.417865i 0 0 0 2.33003 + 1.25338i 0 2.65078 1.40477i 0
1949.3 0 −1.56849 0.734734i 0 0 0 0.156656 2.64111i 0 1.92033 + 2.30485i 0
1949.4 0 −1.56253 + 0.747325i 0 0 0 −2.52603 + 0.786875i 0 1.88301 2.33544i 0
See all 32 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1949.16 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
7.d odd 6 1 inner
15.d odd 2 1 inner
21.g even 6 1 inner
35.i odd 6 1 inner
105.p even 6 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2100.2.bo.i 32
3.b odd 2 1 inner 2100.2.bo.i 32
5.b even 2 1 inner 2100.2.bo.i 32
5.c odd 4 1 2100.2.bi.l 16
5.c odd 4 1 2100.2.bi.m yes 16
7.d odd 6 1 inner 2100.2.bo.i 32
15.d odd 2 1 inner 2100.2.bo.i 32
15.e even 4 1 2100.2.bi.l 16
15.e even 4 1 2100.2.bi.m yes 16
21.g even 6 1 inner 2100.2.bo.i 32
35.i odd 6 1 inner 2100.2.bo.i 32
35.k even 12 1 2100.2.bi.l 16
35.k even 12 1 2100.2.bi.m yes 16
105.p even 6 1 inner 2100.2.bo.i 32
105.w odd 12 1 2100.2.bi.l 16
105.w odd 12 1 2100.2.bi.m yes 16

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2100.2.bi.l 16 5.c odd 4 1
2100.2.bi.l 16 15.e even 4 1
2100.2.bi.l 16 35.k even 12 1
2100.2.bi.l 16 105.w odd 12 1
2100.2.bi.m yes 16 5.c odd 4 1
2100.2.bi.m yes 16 15.e even 4 1
2100.2.bi.m yes 16 35.k even 12 1
2100.2.bi.m yes 16 105.w odd 12 1
2100.2.bo.i 32 1.a even 1 1 trivial
2100.2.bo.i 32 3.b odd 2 1 inner
2100.2.bo.i 32 5.b even 2 1 inner
2100.2.bo.i 32 7.d odd 6 1 inner
2100.2.bo.i 32 15.d odd 2 1 inner
2100.2.bo.i 32 21.g even 6 1 inner
2100.2.bo.i 32 35.i odd 6 1 inner
2100.2.bo.i 32 105.p even 6 1 inner

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(2100, [\chi])$$:

 $$T_{11}^{16} - \cdots$$ $$T_{13}^{8} - 21 T_{13}^{6} + 71 T_{13}^{4} - 78 T_{13}^{2} + 25$$ $$T_{19}^{8} - \cdots$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database