# Properties

 Label 3234.2.e.c Level 3234 Weight 2 Character orbit 3234.e Analytic conductor 25.824 Analytic rank 0 Dimension 24 CM no Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3234.e (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$25.8236200137$$ Analytic rank: $$0$$ Dimension: $$24$$ 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.

 $$\operatorname{Tr}(f)(q) =$$ $$24q - 24q^{4} - 24q^{6} - 24q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$24q - 24q^{4} - 24q^{6} - 24q^{9} + 24q^{16} + 16q^{17} - 32q^{19} - 8q^{22} + 24q^{24} - 8q^{25} - 8q^{33} + 24q^{36} + 16q^{37} - 16q^{41} + 24q^{54} + 16q^{55} - 16q^{62} - 24q^{64} - 64q^{67} - 16q^{68} + 64q^{71} + 32q^{76} + 24q^{81} - 16q^{83} + 8q^{88} - 16q^{93} + 64q^{94} - 24q^{96} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
2155.1 1.00000i 1.00000i −1.00000 3.51377i −1.00000 0 1.00000i −1.00000 −3.51377
2155.2 1.00000i 1.00000i −1.00000 2.84462i −1.00000 0 1.00000i −1.00000 −2.84462
2155.3 1.00000i 1.00000i −1.00000 1.98215i −1.00000 0 1.00000i −1.00000 −1.98215
2155.4 1.00000i 1.00000i −1.00000 1.58222i −1.00000 0 1.00000i −1.00000 −1.58222
2155.5 1.00000i 1.00000i −1.00000 0.942563i −1.00000 0 1.00000i −1.00000 −0.942563
2155.6 1.00000i 1.00000i −1.00000 0.500309i −1.00000 0 1.00000i −1.00000 −0.500309
2155.7 1.00000i 1.00000i −1.00000 0.313884i −1.00000 0 1.00000i −1.00000 0.313884
2155.8 1.00000i 1.00000i −1.00000 0.357203i −1.00000 0 1.00000i −1.00000 0.357203
2155.9 1.00000i 1.00000i −1.00000 0.516505i −1.00000 0 1.00000i −1.00000 0.516505
2155.10 1.00000i 1.00000i −1.00000 2.66749i −1.00000 0 1.00000i −1.00000 2.66749
2155.11 1.00000i 1.00000i −1.00000 3.45711i −1.00000 0 1.00000i −1.00000 3.45711
2155.12 1.00000i 1.00000i −1.00000 4.05345i −1.00000 0 1.00000i −1.00000 4.05345
2155.13 1.00000i 1.00000i −1.00000 4.05345i −1.00000 0 1.00000i −1.00000 4.05345
2155.14 1.00000i 1.00000i −1.00000 3.45711i −1.00000 0 1.00000i −1.00000 3.45711
2155.15 1.00000i 1.00000i −1.00000 2.66749i −1.00000 0 1.00000i −1.00000 2.66749
2155.16 1.00000i 1.00000i −1.00000 0.516505i −1.00000 0 1.00000i −1.00000 0.516505
2155.17 1.00000i 1.00000i −1.00000 0.357203i −1.00000 0 1.00000i −1.00000 0.357203
2155.18 1.00000i 1.00000i −1.00000 0.313884i −1.00000 0 1.00000i −1.00000 0.313884
2155.19 1.00000i 1.00000i −1.00000 0.500309i −1.00000 0 1.00000i −1.00000 −0.500309
2155.20 1.00000i 1.00000i −1.00000 0.942563i −1.00000 0 1.00000i −1.00000 −0.942563
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 2155.24 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
77.b even 2 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 3234.2.e.c 24
7.b odd 2 1 3234.2.e.d yes 24
11.b odd 2 1 3234.2.e.d yes 24
77.b even 2 1 inner 3234.2.e.c 24

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
3234.2.e.c 24 1.a even 1 1 trivial
3234.2.e.c 24 77.b even 2 1 inner
3234.2.e.d yes 24 7.b odd 2 1
3234.2.e.d yes 24 11.b odd 2 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(3234, [\chi])$$:

 $$T_{5}^{24} + \cdots$$ $$T_{13}^{12} - \cdots$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database