Properties

Label 207.6.c.a
Level $207$
Weight $6$
Character orbit 207.c
Analytic conductor $33.199$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 207.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(33.1994507013\)
Analytic rank: \(0\)
Dimension: \(40\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 600 q^{4}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 40 q - 600 q^{4} - 1048 q^{13} + 9728 q^{16} + 14704 q^{25} + 4640 q^{31} - 91864 q^{46} - 8192 q^{49} + 150360 q^{52} + 134592 q^{55} - 195704 q^{58} - 183416 q^{64} - 257448 q^{70} + 31088 q^{73} - 77096 q^{82} - 368760 q^{85} - 123512 q^{94}+O(q^{100}) \) Copy content Toggle raw display

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
206.1 6.22736i 0 −6.78003 −105.915 0 86.6285i 157.054i 0 659.570i
206.2 6.22736i 0 −6.78003 −105.915 0 86.6285i 157.054i 0 659.570i
206.3 1.91117i 0 28.3474 86.4475 0 91.5099i 115.334i 0 165.216i
206.4 1.91117i 0 28.3474 86.4475 0 91.5099i 115.334i 0 165.216i
206.5 10.4484i 0 −77.1695 −72.3402 0 9.31885i 471.949i 0 755.841i
206.6 10.4484i 0 −77.1695 −72.3402 0 9.31885i 471.949i 0 755.841i
206.7 6.00386i 0 −4.04628 −54.7821 0 232.221i 167.830i 0 328.904i
206.8 6.00386i 0 −4.04628 −54.7821 0 232.221i 167.830i 0 328.904i
206.9 3.32542i 0 20.9416 −58.3890 0 22.0963i 176.053i 0 194.168i
206.10 3.32542i 0 20.9416 −58.3890 0 22.0963i 176.053i 0 194.168i
206.11 10.4590i 0 −77.3916 44.1133 0 173.403i 474.753i 0 461.383i
206.12 10.4590i 0 −77.3916 44.1133 0 173.403i 474.753i 0 461.383i
206.13 7.94564i 0 −31.1332 −36.1472 0 129.914i 6.88755i 0 287.213i
206.14 7.94564i 0 −31.1332 −36.1472 0 129.914i 6.88755i 0 287.213i
206.15 8.84990i 0 −46.3207 −32.1196 0 32.0928i 126.737i 0 284.255i
206.16 8.84990i 0 −46.3207 −32.1196 0 32.0928i 126.737i 0 284.255i
206.17 1.13533i 0 30.7110 −11.6464 0 79.1972i 71.1980i 0 13.2226i
206.18 1.13533i 0 30.7110 −11.6464 0 79.1972i 71.1980i 0 13.2226i
206.19 4.37708i 0 12.8412 −13.0959 0 213.282i 196.273i 0 57.3218i
206.20 4.37708i 0 12.8412 −13.0959 0 213.282i 196.273i 0 57.3218i
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 206.40
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
23.b odd 2 1 inner
69.c even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 207.6.c.a 40
3.b odd 2 1 inner 207.6.c.a 40
23.b odd 2 1 inner 207.6.c.a 40
69.c even 2 1 inner 207.6.c.a 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
207.6.c.a 40 1.a even 1 1 trivial
207.6.c.a 40 3.b odd 2 1 inner
207.6.c.a 40 23.b odd 2 1 inner
207.6.c.a 40 69.c even 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{6}^{\mathrm{new}}(207, [\chi])\).