Properties

Label 207.6.i
Level $207$
Weight $6$
Character orbit 207.i
Rep. character $\chi_{207}(55,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $490$
Sturm bound $144$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 207.i (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(144\)

Dimensions

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

Total New Old
Modular forms 1240 510 730
Cusp forms 1160 490 670
Eisenstein series 80 20 60

Trace form

\( 490 q + 7 q^{2} - 819 q^{4} + 39 q^{5} - 29 q^{7} + 272 q^{8} + O(q^{10}) \) \( 490 q + 7 q^{2} - 819 q^{4} + 39 q^{5} - 29 q^{7} + 272 q^{8} + 355 q^{10} - 1039 q^{11} - 735 q^{13} - 561 q^{14} - 9995 q^{16} + 2962 q^{17} + 4610 q^{19} - 3717 q^{20} - 9498 q^{22} - 9384 q^{23} - 18016 q^{25} + 8184 q^{26} + 27235 q^{28} + 23050 q^{29} - 5978 q^{31} - 35169 q^{32} + 83261 q^{34} - 25219 q^{35} - 77851 q^{37} + 55646 q^{38} + 33907 q^{40} + 281 q^{41} + 51757 q^{43} - 135536 q^{44} + 164869 q^{46} - 45222 q^{47} - 140802 q^{49} - 2404 q^{50} - 215936 q^{52} + 34663 q^{53} - 84277 q^{55} + 49010 q^{56} - 44411 q^{58} - 377799 q^{59} - 148353 q^{61} - 117448 q^{62} - 227262 q^{64} + 108904 q^{65} + 169665 q^{67} + 614718 q^{68} + 243566 q^{70} + 262754 q^{71} - 13145 q^{73} - 386428 q^{74} - 433630 q^{76} - 219404 q^{77} - 61647 q^{79} + 121330 q^{80} + 364354 q^{82} + 369534 q^{83} + 261341 q^{85} + 352439 q^{86} - 194823 q^{88} - 287089 q^{89} - 249052 q^{91} - 763276 q^{92} - 1041709 q^{94} - 775704 q^{95} - 224380 q^{97} + 73483 q^{98} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(207, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)