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Properties

Label 207.8.k
Level $207$
Weight $8$
Character orbit 207.k
Rep. character $\chi_{207}(17,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $560$
Sturm bound $192$

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Defining parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 207.k (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(207, [\chi])\).

Total New Old
Modular forms 1720 560 1160
Cusp forms 1640 560 1080
Eisenstein series 80 0 80

Trace form

\( 560 q + 3480 q^{4} + O(q^{10}) \) \( 560 q + 3480 q^{4} - 9976 q^{13} - 211072 q^{16} - 1023728 q^{25} - 682336 q^{31} - 3631892 q^{34} + 1810424 q^{37} - 2931500 q^{40} + 3388616 q^{43} + 16801224 q^{46} + 10091488 q^{49} - 27822148 q^{52} + 4439044 q^{55} + 12632388 q^{58} + 22205656 q^{61} + 23324856 q^{64} - 12063172 q^{67} - 4720792 q^{70} + 5840764 q^{73} + 85302272 q^{76} + 2313784 q^{79} - 97982488 q^{82} - 25431724 q^{85} + 2574712 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(207, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(207, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(207, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)