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Properties

Label 207.8.o
Level $207$
Weight $8$
Character orbit 207.o
Rep. character $\chi_{207}(5,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $3320$
Sturm bound $192$

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Defining parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 207.o (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(192\)

Dimensions

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

Total New Old
Modular forms 3400 3400 0
Cusp forms 3320 3320 0
Eisenstein series 80 80 0

Trace form

\( 3320 q - 27 q^{2} + 8 q^{3} - 10505 q^{4} - 33 q^{5} - 1531 q^{6} - 11 q^{7} + 632 q^{9} + O(q^{10}) \) \( 3320 q - 27 q^{2} + 8 q^{3} - 10505 q^{4} - 33 q^{5} - 1531 q^{6} - 11 q^{7} + 632 q^{9} - 44 q^{10} - 33 q^{11} - 22810 q^{12} - 9 q^{13} - 33 q^{14} + 7656 q^{15} + 655095 q^{16} - 250077 q^{18} - 44 q^{19} - 33 q^{20} + 221705 q^{21} - 73791 q^{23} - 442196 q^{24} + 2396747 q^{25} - 9475 q^{27} - 44 q^{28} + 756243 q^{29} + 1480842 q^{30} + 198645 q^{31} + 400485 q^{32} + 2430384 q^{33} - 11 q^{34} - 1160329 q^{36} - 44 q^{37} - 33 q^{38} + 1635776 q^{39} - 4397261 q^{40} + 1566225 q^{41} - 22 q^{42} - 11 q^{43} + 1684476 q^{46} - 2181720 q^{47} - 3228452 q^{48} - 15189913 q^{49} + 2700969 q^{50} - 22 q^{51} + 1055986 q^{52} + 14963676 q^{54} - 3011804 q^{55} - 56669217 q^{56} - 7508941 q^{57} - 1294264 q^{58} + 10404927 q^{59} + 21971818 q^{60} - 11 q^{61} + 9022893 q^{63} + 69533186 q^{64} - 16648434 q^{65} - 16582863 q^{66} - 11 q^{67} - 4427385 q^{69} - 3123862 q^{70} + 32517788 q^{72} - 36 q^{73} + 91008159 q^{74} + 10526879 q^{75} - 11 q^{76} + 20832375 q^{77} + 83919351 q^{78} - 11 q^{79} + 37854532 q^{81} + 1782602 q^{82} - 88148346 q^{83} - 124183400 q^{84} + 156241 q^{85} - 33 q^{86} + 10659068 q^{87} - 360459 q^{88} - 284593496 q^{90} - 76552227 q^{92} + 115004740 q^{93} - 7377828 q^{94} - 63770637 q^{95} - 6148318 q^{96} - 31930250 q^{97} + 271367954 q^{99} + O(q^{100}) \)

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.