Properties

 Label 8028.2.h.a Level 8028 Weight 2 Character orbit 8028.h Analytic conductor 64.104 Analytic rank 0 Dimension 76 CM No

Related objects

Newspace parameters

 Level: $$N$$ = $$8028 = 2^{2} \cdot 3^{2} \cdot 223$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 8028.h (of order $$2$$ and degree $$1$$)

Newform invariants

 Self dual: No Analytic conductor: $$64.1039027427$$ Analytic rank: $$0$$ Dimension: $$76$$ 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.

 $$\operatorname{Tr}(f)(q) =$$ $$76q$$ $$\mathstrut +\mathstrut 8q^{7}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$76q$$ $$\mathstrut +\mathstrut 8q^{7}$$ $$\mathstrut +\mathstrut 16q^{19}$$ $$\mathstrut +\mathstrut 100q^{25}$$ $$\mathstrut -\mathstrut 8q^{31}$$ $$\mathstrut +\mathstrut 32q^{37}$$ $$\mathstrut -\mathstrut 24q^{43}$$ $$\mathstrut +\mathstrut 68q^{49}$$ $$\mathstrut +\mathstrut 24q^{55}$$ $$\mathstrut +\mathstrut 8q^{73}$$ $$\mathstrut +\mathstrut O(q^{100})$$

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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
4013.1 0 0 0 −4.23105 0 2.43977 0 0 0
4013.2 0 0 0 −4.23105 0 2.43977 0 0 0
4013.3 0 0 0 −3.84036 0 1.75909 0 0 0
4013.4 0 0 0 −3.84036 0 1.75909 0 0 0
4013.5 0 0 0 −3.83180 0 −1.12103 0 0 0
4013.6 0 0 0 −3.83180 0 −1.12103 0 0 0
4013.7 0 0 0 −3.80256 0 0.208948 0 0 0
4013.8 0 0 0 −3.80256 0 0.208948 0 0 0
4013.9 0 0 0 −3.65965 0 −4.62592 0 0 0
4013.10 0 0 0 −3.65965 0 −4.62592 0 0 0
4013.11 0 0 0 −2.81288 0 3.64674 0 0 0
4013.12 0 0 0 −2.81288 0 3.64674 0 0 0
4013.13 0 0 0 −2.68681 0 −3.11614 0 0 0
4013.14 0 0 0 −2.68681 0 −3.11614 0 0 0
4013.15 0 0 0 −2.24499 0 −1.57279 0 0 0
4013.16 0 0 0 −2.24499 0 −1.57279 0 0 0
4013.17 0 0 0 −2.12158 0 2.81365 0 0 0
4013.18 0 0 0 −2.12158 0 2.81365 0 0 0
4013.19 0 0 0 −1.82157 0 −3.59530 0 0 0
4013.20 0 0 0 −1.82157 0 −3.59530 0 0 0
See all 76 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 4013.76 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

There are no other newforms in $$S_{2}^{\mathrm{new}}(8028, [\chi])$$.