↑

Properties

Label 207.6.k
Level $207$
Weight $6$
Character orbit 207.k
Rep. character $\chi_{207}(17,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $400$
Sturm bound $144$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 207.k (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(144\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(207, [\chi])\).

Total New Old
Modular forms 1240 400 840
Cusp forms 1160 400 760
Eisenstein series 80 0 80

Trace form

\( 400 q + 600 q^{4} + O(q^{10}) \) \( 400 q + 600 q^{4} + 1048 q^{13} - 9728 q^{16} - 14704 q^{25} - 4640 q^{31} - 152020 q^{34} + 144232 q^{37} + 34100 q^{40} - 118712 q^{43} - 256440 q^{46} + 8192 q^{49} + 408220 q^{52} + 334052 q^{55} - 270300 q^{58} - 250360 q^{61} + 408696 q^{64} + 188716 q^{67} + 974824 q^{70} - 10012 q^{73} - 830720 q^{76} - 685960 q^{79} - 193592 q^{82} + 1119004 q^{85} + 123512 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(207, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(207, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(207, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)