Properties

Label 2100.2.bo.i
Level 2100
Weight 2
Character orbit 2100.bo
Analytic conductor 16.769
Analytic rank 0
Dimension 32
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.bo (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(16.7685844245\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32q + 18q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 32q + 18q^{9} + 36q^{19} - 22q^{21} - 36q^{31} - 24q^{39} + 36q^{49} - 2q^{51} + 72q^{61} + 14q^{81} + 40q^{91} + 60q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1349.1 0 −1.68420 + 0.404332i 0 0 0 2.10133 1.60761i 0 2.67303 1.36195i 0
1349.2 0 −1.68089 0.417865i 0 0 0 2.33003 1.25338i 0 2.65078 + 1.40477i 0
1349.3 0 −1.56849 + 0.734734i 0 0 0 0.156656 + 2.64111i 0 1.92033 2.30485i 0
1349.4 0 −1.56253 0.747325i 0 0 0 −2.52603 0.786875i 0 1.88301 + 2.33544i 0
1349.5 0 −1.42054 + 0.990987i 0 0 0 −0.156656 2.64111i 0 1.03589 2.81548i 0
1349.6 0 −1.19226 + 1.25639i 0 0 0 −2.10133 + 1.60761i 0 −0.157032 2.99589i 0
1349.7 0 −0.478563 + 1.66463i 0 0 0 −2.33003 + 1.25338i 0 −2.54196 1.59326i 0
1349.8 0 −0.134063 + 1.72685i 0 0 0 2.52603 + 0.786875i 0 −2.96405 0.463016i 0
1349.9 0 0.134063 1.72685i 0 0 0 −2.52603 0.786875i 0 −2.96405 0.463016i 0
1349.10 0 0.478563 1.66463i 0 0 0 2.33003 1.25338i 0 −2.54196 1.59326i 0
1349.11 0 1.19226 1.25639i 0 0 0 2.10133 1.60761i 0 −0.157032 2.99589i 0
1349.12 0 1.42054 0.990987i 0 0 0 0.156656 + 2.64111i 0 1.03589 2.81548i 0
1349.13 0 1.56253 + 0.747325i 0 0 0 2.52603 + 0.786875i 0 1.88301 + 2.33544i 0
1349.14 0 1.56849 0.734734i 0 0 0 −0.156656 2.64111i 0 1.92033 2.30485i 0
1349.15 0 1.68089 + 0.417865i 0 0 0 −2.33003 + 1.25338i 0 2.65078 + 1.40477i 0
1349.16 0 1.68420 0.404332i 0 0 0 −2.10133 + 1.60761i 0 2.67303 1.36195i 0
1949.1 0 −1.68420 0.404332i 0 0 0 2.10133 + 1.60761i 0 2.67303 + 1.36195i 0
1949.2 0 −1.68089 + 0.417865i 0 0 0 2.33003 + 1.25338i 0 2.65078 1.40477i 0
1949.3 0 −1.56849 0.734734i 0 0 0 0.156656 2.64111i 0 1.92033 + 2.30485i 0
1949.4 0 −1.56253 + 0.747325i 0 0 0 −2.52603 + 0.786875i 0 1.88301 2.33544i 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1949.16
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.b even 2 1 inner
7.d odd 6 1 inner
15.d odd 2 1 inner
21.g even 6 1 inner
35.i odd 6 1 inner
105.p even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2100.2.bo.i 32
3.b odd 2 1 inner 2100.2.bo.i 32
5.b even 2 1 inner 2100.2.bo.i 32
5.c odd 4 1 2100.2.bi.l 16
5.c odd 4 1 2100.2.bi.m yes 16
7.d odd 6 1 inner 2100.2.bo.i 32
15.d odd 2 1 inner 2100.2.bo.i 32
15.e even 4 1 2100.2.bi.l 16
15.e even 4 1 2100.2.bi.m yes 16
21.g even 6 1 inner 2100.2.bo.i 32
35.i odd 6 1 inner 2100.2.bo.i 32
35.k even 12 1 2100.2.bi.l 16
35.k even 12 1 2100.2.bi.m yes 16
105.p even 6 1 inner 2100.2.bo.i 32
105.w odd 12 1 2100.2.bi.l 16
105.w odd 12 1 2100.2.bi.m yes 16
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2100.2.bi.l 16 5.c odd 4 1
2100.2.bi.l 16 15.e even 4 1
2100.2.bi.l 16 35.k even 12 1
2100.2.bi.l 16 105.w odd 12 1
2100.2.bi.m yes 16 5.c odd 4 1
2100.2.bi.m yes 16 15.e even 4 1
2100.2.bi.m yes 16 35.k even 12 1
2100.2.bi.m yes 16 105.w odd 12 1
2100.2.bo.i 32 1.a even 1 1 trivial
2100.2.bo.i 32 3.b odd 2 1 inner
2100.2.bo.i 32 5.b even 2 1 inner
2100.2.bo.i 32 7.d odd 6 1 inner
2100.2.bo.i 32 15.d odd 2 1 inner
2100.2.bo.i 32 21.g even 6 1 inner
2100.2.bo.i 32 35.i odd 6 1 inner
2100.2.bo.i 32 105.p even 6 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(2100, [\chi])\):

\(T_{11}^{16} - \cdots\)
\( T_{13}^{8} - 21 T_{13}^{6} + 71 T_{13}^{4} - 78 T_{13}^{2} + 25 \)
\(T_{19}^{8} - \cdots\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database