Properties

Label 3150.2.bf.e
Level 3150
Weight 2
Character orbit 3150.bf
Analytic conductor 25.153
Analytic rank 0
Dimension 24
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.bf (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 24q + 12q^{4} + 4q^{7} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 24q + 12q^{4} + 4q^{7} - 12q^{16} + 12q^{19} - 4q^{28} - 28q^{37} - 96q^{43} - 8q^{46} - 52q^{49} + 12q^{52} - 8q^{58} - 12q^{61} - 24q^{64} + 4q^{67} + 12q^{73} + 4q^{79} + 68q^{91} - 24q^{94} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1151.1 −0.866025 + 0.500000i 0 0.500000 0.866025i 0 0 1.52781 2.16005i 1.00000i 0 0
1151.2 −0.866025 + 0.500000i 0 0.500000 0.866025i 0 0 −2.34325 1.22849i 1.00000i 0 0
1151.3 −0.866025 + 0.500000i 0 0.500000 0.866025i 0 0 −0.295801 + 2.62916i 1.00000i 0 0
1151.4 −0.866025 + 0.500000i 0 0.500000 0.866025i 0 0 0.397202 + 2.61577i 1.00000i 0 0
1151.5 −0.866025 + 0.500000i 0 0.500000 0.866025i 0 0 2.43194 1.04195i 1.00000i 0 0
1151.6 −0.866025 + 0.500000i 0 0.500000 0.866025i 0 0 −0.717905 2.54649i 1.00000i 0 0
1151.7 0.866025 0.500000i 0 0.500000 0.866025i 0 0 −0.717905 2.54649i 1.00000i 0 0
1151.8 0.866025 0.500000i 0 0.500000 0.866025i 0 0 2.43194 1.04195i 1.00000i 0 0
1151.9 0.866025 0.500000i 0 0.500000 0.866025i 0 0 0.397202 + 2.61577i 1.00000i 0 0
1151.10 0.866025 0.500000i 0 0.500000 0.866025i 0 0 −0.295801 + 2.62916i 1.00000i 0 0
1151.11 0.866025 0.500000i 0 0.500000 0.866025i 0 0 −2.34325 1.22849i 1.00000i 0 0
1151.12 0.866025 0.500000i 0 0.500000 0.866025i 0 0 1.52781 2.16005i 1.00000i 0 0
1601.1 −0.866025 0.500000i 0 0.500000 + 0.866025i 0 0 1.52781 + 2.16005i 1.00000i 0 0
1601.2 −0.866025 0.500000i 0 0.500000 + 0.866025i 0 0 −2.34325 + 1.22849i 1.00000i 0 0
1601.3 −0.866025 0.500000i 0 0.500000 + 0.866025i 0 0 −0.295801 2.62916i 1.00000i 0 0
1601.4 −0.866025 0.500000i 0 0.500000 + 0.866025i 0 0 0.397202 2.61577i 1.00000i 0 0
1601.5 −0.866025 0.500000i 0 0.500000 + 0.866025i 0 0 2.43194 + 1.04195i 1.00000i 0 0
1601.6 −0.866025 0.500000i 0 0.500000 + 0.866025i 0 0 −0.717905 + 2.54649i 1.00000i 0 0
1601.7 0.866025 + 0.500000i 0 0.500000 + 0.866025i 0 0 −0.717905 + 2.54649i 1.00000i 0 0
1601.8 0.866025 + 0.500000i 0 0.500000 + 0.866025i 0 0 2.43194 + 1.04195i 1.00000i 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1601.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
7.d odd 6 1 inner
21.g even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 3150.2.bf.e yes 24
3.b odd 2 1 inner 3150.2.bf.e yes 24
5.b even 2 1 3150.2.bf.d 24
5.c odd 4 1 3150.2.bp.g 24
5.c odd 4 1 3150.2.bp.h 24
7.d odd 6 1 inner 3150.2.bf.e yes 24
15.d odd 2 1 3150.2.bf.d 24
15.e even 4 1 3150.2.bp.g 24
15.e even 4 1 3150.2.bp.h 24
21.g even 6 1 inner 3150.2.bf.e yes 24
35.i odd 6 1 3150.2.bf.d 24
35.k even 12 1 3150.2.bp.g 24
35.k even 12 1 3150.2.bp.h 24
105.p even 6 1 3150.2.bf.d 24
105.w odd 12 1 3150.2.bp.g 24
105.w odd 12 1 3150.2.bp.h 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
3150.2.bf.d 24 5.b even 2 1
3150.2.bf.d 24 15.d odd 2 1
3150.2.bf.d 24 35.i odd 6 1
3150.2.bf.d 24 105.p even 6 1
3150.2.bf.e yes 24 1.a even 1 1 trivial
3150.2.bf.e yes 24 3.b odd 2 1 inner
3150.2.bf.e yes 24 7.d odd 6 1 inner
3150.2.bf.e yes 24 21.g even 6 1 inner
3150.2.bp.g 24 5.c odd 4 1
3150.2.bp.g 24 15.e even 4 1
3150.2.bp.g 24 35.k even 12 1
3150.2.bp.g 24 105.w odd 12 1
3150.2.bp.h 24 5.c odd 4 1
3150.2.bp.h 24 15.e even 4 1
3150.2.bp.h 24 35.k even 12 1
3150.2.bp.h 24 105.w odd 12 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(3150, [\chi])\):

\(T_{11}^{24} - \cdots\)
\(T_{37}^{12} + \cdots\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database