# Properties

 Label 4032.2.i.c Level 4032 Weight 2 Character orbit 4032.i Analytic conductor 32.196 Analytic rank 0 Dimension 48 CM No

# Related objects

## Newspace parameters

 Level: $$N$$ = $$4032 = 2^{6} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4032.i (of order $$2$$ and degree $$1$$)

## Newform invariants

 Self dual: No Analytic conductor: $$32.195682095$$ Analytic rank: $$0$$ Dimension: $$48$$ 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.

 $$\operatorname{Tr}(f)(q) =$$ $$48q$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$48q$$ $$\mathstrut -\mathstrut 80q^{25}$$ $$\mathstrut -\mathstrut 16q^{49}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1889.1 0 0 0 1.77767i 0 −2.39248 1.12962i 0 0 0
1889.2 0 0 0 1.77767i 0 −2.39248 + 1.12962i 0 0 0
1889.3 0 0 0 1.21807i 0 0.355387 2.62177i 0 0 0
1889.4 0 0 0 1.21807i 0 0.355387 + 2.62177i 0 0 0
1889.5 0 0 0 1.77767i 0 −2.39248 1.12962i 0 0 0
1889.6 0 0 0 1.77767i 0 −2.39248 + 1.12962i 0 0 0
1889.7 0 0 0 3.91870i 0 2.03709 1.68827i 0 0 0
1889.8 0 0 0 3.91870i 0 2.03709 + 1.68827i 0 0 0
1889.9 0 0 0 1.21807i 0 0.355387 + 2.62177i 0 0 0
1889.10 0 0 0 1.21807i 0 0.355387 2.62177i 0 0 0
1889.11 0 0 0 1.77767i 0 2.39248 1.12962i 0 0 0
1889.12 0 0 0 1.77767i 0 2.39248 + 1.12962i 0 0 0
1889.13 0 0 0 3.91870i 0 2.03709 1.68827i 0 0 0
1889.14 0 0 0 3.91870i 0 2.03709 + 1.68827i 0 0 0
1889.15 0 0 0 3.91870i 0 2.03709 + 1.68827i 0 0 0
1889.16 0 0 0 3.91870i 0 2.03709 1.68827i 0 0 0
1889.17 0 0 0 3.91870i 0 −2.03709 1.68827i 0 0 0
1889.18 0 0 0 3.91870i 0 −2.03709 + 1.68827i 0 0 0
1889.19 0 0 0 1.77767i 0 −2.39248 + 1.12962i 0 0 0
1889.20 0 0 0 1.77767i 0 −2.39248 1.12962i 0 0 0
See all 48 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1889.48 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

This newform does not have CM; other inner twists have not been computed.

## Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(4032, \chi)$$:

 $$T_{5}^{6}$$ $$\mathstrut +\mathstrut 20 T_{5}^{4}$$ $$\mathstrut +\mathstrut 76 T_{5}^{2}$$ $$\mathstrut +\mathstrut 72$$ $$T_{47}^{6}$$ $$\mathstrut -\mathstrut 128 T_{47}^{4}$$ $$\mathstrut +\mathstrut 3520 T_{47}^{2}$$ $$\mathstrut -\mathstrut 4608$$