Properties

Label 2100.2.s.c
Level 2100
Weight 2
Character orbit 2100.s
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.s (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(16.7685844245\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 32q + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 32q - 8q^{21} + 48q^{31} - 32q^{51} + 16q^{61} + 64q^{81} + 32q^{91} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1457.1 0 −1.73156 0.0412661i 0 0 0 0.707107 + 0.707107i 0 2.99659 + 0.142909i 0
1457.2 0 −1.69214 + 0.369667i 0 0 0 0.707107 + 0.707107i 0 2.72669 1.25106i 0
1457.3 0 −1.63431 + 0.573626i 0 0 0 −0.707107 0.707107i 0 2.34191 1.87496i 0
1457.4 0 −1.28800 1.15804i 0 0 0 −0.707107 0.707107i 0 0.317883 + 2.98311i 0
1457.5 0 −1.15804 1.28800i 0 0 0 0.707107 + 0.707107i 0 −0.317883 + 2.98311i 0
1457.6 0 −0.573626 + 1.63431i 0 0 0 −0.707107 0.707107i 0 −2.34191 1.87496i 0
1457.7 0 −0.369667 + 1.69214i 0 0 0 0.707107 + 0.707107i 0 −2.72669 1.25106i 0
1457.8 0 −0.0412661 1.73156i 0 0 0 −0.707107 0.707107i 0 −2.99659 + 0.142909i 0
1457.9 0 0.0412661 + 1.73156i 0 0 0 0.707107 + 0.707107i 0 −2.99659 + 0.142909i 0
1457.10 0 0.369667 1.69214i 0 0 0 −0.707107 0.707107i 0 −2.72669 1.25106i 0
1457.11 0 0.573626 1.63431i 0 0 0 0.707107 + 0.707107i 0 −2.34191 1.87496i 0
1457.12 0 1.15804 + 1.28800i 0 0 0 −0.707107 0.707107i 0 −0.317883 + 2.98311i 0
1457.13 0 1.28800 + 1.15804i 0 0 0 0.707107 + 0.707107i 0 0.317883 + 2.98311i 0
1457.14 0 1.63431 0.573626i 0 0 0 0.707107 + 0.707107i 0 2.34191 1.87496i 0
1457.15 0 1.69214 0.369667i 0 0 0 −0.707107 0.707107i 0 2.72669 1.25106i 0
1457.16 0 1.73156 + 0.0412661i 0 0 0 −0.707107 0.707107i 0 2.99659 + 0.142909i 0
1793.1 0 −1.73156 + 0.0412661i 0 0 0 0.707107 0.707107i 0 2.99659 0.142909i 0
1793.2 0 −1.69214 0.369667i 0 0 0 0.707107 0.707107i 0 2.72669 + 1.25106i 0
1793.3 0 −1.63431 0.573626i 0 0 0 −0.707107 + 0.707107i 0 2.34191 + 1.87496i 0
1793.4 0 −1.28800 + 1.15804i 0 0 0 −0.707107 + 0.707107i 0 0.317883 2.98311i 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1793.16
Significant digits:
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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
5.c odd 4 2 inner
15.d odd 2 1 inner
15.e even 4 2 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2100.2.s.c 32
3.b odd 2 1 inner 2100.2.s.c 32
5.b even 2 1 inner 2100.2.s.c 32
5.c odd 4 2 inner 2100.2.s.c 32
15.d odd 2 1 inner 2100.2.s.c 32
15.e even 4 2 inner 2100.2.s.c 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2100.2.s.c 32 1.a even 1 1 trivial
2100.2.s.c 32 3.b odd 2 1 inner
2100.2.s.c 32 5.b even 2 1 inner
2100.2.s.c 32 5.c odd 4 2 inner
2100.2.s.c 32 15.d odd 2 1 inner
2100.2.s.c 32 15.e even 4 2 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{11}^{8} + 60 T_{11}^{6} + 962 T_{11}^{4} + 4452 T_{11}^{2} + 6253 \) acting on \(S_{2}^{\mathrm{new}}(2100, [\chi])\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database