# Properties

 Label 2151.2.b.a Level $2151$ Weight $2$ Character orbit 2151.b Analytic conductor $17.176$ Analytic rank $0$ Dimension $80$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2151 = 3^{2} \cdot 239$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2151.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$17.1758214748$$ Analytic rank: $$0$$ Dimension: $$80$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## $q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$80q - 80q^{4} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$80q - 80q^{4} + 16q^{10} + 56q^{16} + 40q^{22} - 64q^{25} - 8q^{31} + 32q^{34} - 24q^{40} - 104q^{49} - 24q^{55} + 56q^{58} + 40q^{61} - 80q^{64} - 8q^{67} - 8q^{85} - 120q^{88} + 32q^{91} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
2150.1 2.75120i 0 −5.56908 1.21173i 0 4.92033i 9.81922i 0 −3.33371
2150.2 2.75120i 0 −5.56908 1.21173i 0 4.92033i 9.81922i 0 −3.33371
2150.3 2.56329i 0 −4.57046 2.12793i 0 2.62545i 6.58884i 0 −5.45450
2150.4 2.56329i 0 −4.57046 2.12793i 0 2.62545i 6.58884i 0 −5.45450
2150.5 2.54042i 0 −4.45371 2.74390i 0 3.15846i 6.23344i 0 6.97064
2150.6 2.54042i 0 −4.45371 2.74390i 0 3.15846i 6.23344i 0 6.97064
2150.7 2.53879i 0 −4.44547 1.00261i 0 0.202697i 6.20855i 0 2.54543
2150.8 2.53879i 0 −4.44547 1.00261i 0 0.202697i 6.20855i 0 2.54543
2150.9 2.23937i 0 −3.01478 3.12574i 0 3.32975i 2.27247i 0 6.99969
2150.10 2.23937i 0 −3.01478 3.12574i 0 3.32975i 2.27247i 0 6.99969
2150.11 2.14709i 0 −2.61000 2.81441i 0 1.25298i 1.30973i 0 6.04279
2150.12 2.14709i 0 −2.61000 2.81441i 0 1.25298i 1.30973i 0 6.04279
2150.13 2.04427i 0 −2.17903 3.47846i 0 3.44491i 0.365980i 0 −7.11089
2150.14 2.04427i 0 −2.17903 3.47846i 0 3.44491i 0.365980i 0 −7.11089
2150.15 1.83893i 0 −1.38165 0.488895i 0 1.94727i 1.13709i 0 −0.899043
2150.16 1.83893i 0 −1.38165 0.488895i 0 1.94727i 1.13709i 0 −0.899043
2150.17 1.79525i 0 −1.22293 1.07382i 0 2.61327i 1.39503i 0 −1.92778
2150.18 1.79525i 0 −1.22293 1.07382i 0 2.61327i 1.39503i 0 −1.92778
2150.19 1.73293i 0 −1.00304 1.48937i 0 1.62864i 1.72766i 0 −2.58096
2150.20 1.73293i 0 −1.00304 1.48937i 0 1.62864i 1.72766i 0 −2.58096
See all 80 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 2150.80 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
239.b odd 2 1 inner
717.b even 2 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2151.2.b.a 80
3.b odd 2 1 inner 2151.2.b.a 80
239.b odd 2 1 inner 2151.2.b.a 80
717.b even 2 1 inner 2151.2.b.a 80

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2151.2.b.a 80 1.a even 1 1 trivial
2151.2.b.a 80 3.b odd 2 1 inner
2151.2.b.a 80 239.b odd 2 1 inner
2151.2.b.a 80 717.b even 2 1 inner

## Hecke kernels

This newform subspace is the entire newspace $$S_{2}^{\mathrm{new}}(2151, [\chi])$$.