# Properties

 Label 1120.2.bz.e Level $1120$ Weight $2$ Character orbit 1120.bz Analytic conductor $8.943$ Analytic rank $0$ Dimension $24$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1120 = 2^{5} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1120.bz (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.94324502638$$ Analytic rank: $$0$$ Dimension: $$24$$ Relative dimension: $$12$$ over $$\Q(\zeta_{6})$$ Twist minimal: no (minimal twist has level 280) 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.

 $$\operatorname{Tr}(f)(q) =$$ $$24q - 12q^{3} - 12q^{5} - 10q^{7} + 12q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$24q - 12q^{3} - 12q^{5} - 10q^{7} + 12q^{9} - 8q^{11} + 20q^{13} + 6q^{17} - 18q^{19} - 26q^{21} - 18q^{23} - 12q^{25} + 6q^{31} + 12q^{33} + 8q^{35} + 18q^{39} - 32q^{43} + 12q^{45} + 8q^{49} + 22q^{51} + 30q^{53} + 16q^{55} - 44q^{57} + 18q^{59} + 22q^{61} + 12q^{63} - 10q^{65} + 8q^{67} - 12q^{69} + 30q^{73} + 12q^{75} - 32q^{77} - 6q^{79} - 4q^{81} - 14q^{87} - 60q^{89} - 18q^{91} - 18q^{93} + 18q^{95} + 56q^{99} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
271.1 0 −2.75363 + 1.58981i 0 −0.500000 + 0.866025i 0 1.04250 + 2.43170i 0 3.55500 6.15745i 0
271.2 0 −2.26702 + 1.30886i 0 −0.500000 + 0.866025i 0 −1.72615 2.00510i 0 1.92625 3.33637i 0
271.3 0 −1.94732 + 1.12428i 0 −0.500000 + 0.866025i 0 −2.47009 + 0.947962i 0 1.02803 1.78060i 0
271.4 0 −1.90624 + 1.10057i 0 −0.500000 + 0.866025i 0 0.584379 + 2.58041i 0 0.922503 1.59782i 0
271.5 0 −1.75472 + 1.01309i 0 −0.500000 + 0.866025i 0 1.63843 2.07739i 0 0.552704 0.957311i 0
271.6 0 −0.784482 + 0.452921i 0 −0.500000 + 0.866025i 0 −1.23347 2.34063i 0 −1.08973 + 1.88746i 0
271.7 0 −0.725648 + 0.418953i 0 −0.500000 + 0.866025i 0 2.36913 1.17781i 0 −1.14896 + 1.99005i 0
271.8 0 0.219454 0.126702i 0 −0.500000 + 0.866025i 0 −0.978876 + 2.45801i 0 −1.46789 + 2.54247i 0
271.9 0 0.502680 0.290223i 0 −0.500000 + 0.866025i 0 2.63362 0.253028i 0 −1.33154 + 2.30630i 0
271.10 0 0.908317 0.524417i 0 −0.500000 + 0.866025i 0 −2.14799 1.54472i 0 −0.949974 + 1.64540i 0
271.11 0 1.84104 1.06293i 0 −0.500000 + 0.866025i 0 −2.17552 1.50569i 0 0.759621 1.31570i 0
271.12 0 2.66758 1.54013i 0 −0.500000 + 0.866025i 0 −2.53597 + 0.754231i 0 3.24397 5.61873i 0
591.1 0 −2.75363 1.58981i 0 −0.500000 0.866025i 0 1.04250 2.43170i 0 3.55500 + 6.15745i 0
591.2 0 −2.26702 1.30886i 0 −0.500000 0.866025i 0 −1.72615 + 2.00510i 0 1.92625 + 3.33637i 0
591.3 0 −1.94732 1.12428i 0 −0.500000 0.866025i 0 −2.47009 0.947962i 0 1.02803 + 1.78060i 0
591.4 0 −1.90624 1.10057i 0 −0.500000 0.866025i 0 0.584379 2.58041i 0 0.922503 + 1.59782i 0
591.5 0 −1.75472 1.01309i 0 −0.500000 0.866025i 0 1.63843 + 2.07739i 0 0.552704 + 0.957311i 0
591.6 0 −0.784482 0.452921i 0 −0.500000 0.866025i 0 −1.23347 + 2.34063i 0 −1.08973 1.88746i 0
591.7 0 −0.725648 0.418953i 0 −0.500000 0.866025i 0 2.36913 + 1.17781i 0 −1.14896 1.99005i 0
591.8 0 0.219454 + 0.126702i 0 −0.500000 0.866025i 0 −0.978876 2.45801i 0 −1.46789 2.54247i 0
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 591.12 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
56.m even 6 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1120.2.bz.e 24
4.b odd 2 1 280.2.bj.f yes 24
7.d odd 6 1 1120.2.bz.f 24
8.b even 2 1 280.2.bj.e 24
8.d odd 2 1 1120.2.bz.f 24
28.f even 6 1 280.2.bj.e 24
56.j odd 6 1 280.2.bj.f yes 24
56.m even 6 1 inner 1120.2.bz.e 24

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
280.2.bj.e 24 8.b even 2 1
280.2.bj.e 24 28.f even 6 1
280.2.bj.f yes 24 4.b odd 2 1
280.2.bj.f yes 24 56.j odd 6 1
1120.2.bz.e 24 1.a even 1 1 trivial
1120.2.bz.e 24 56.m even 6 1 inner
1120.2.bz.f 24 7.d odd 6 1
1120.2.bz.f 24 8.d odd 2 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(1120, [\chi])$$:

 $$T_{3}^{24} + \cdots$$ $$T_{13}^{12} - \cdots$$