Properties

Label 207.6.m
Level $207$
Weight $6$
Character orbit 207.m
Rep. character $\chi_{207}(4,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $2360$
Sturm bound $144$

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Defining parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 207.m (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{33})\)
Sturm bound: \(144\)

Dimensions

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

Total New Old
Modular forms 2440 2440 0
Cusp forms 2360 2360 0
Eisenstein series 80 80 0

Trace form

\( 2360 q - 9 q^{2} - 20 q^{3} + 1847 q^{4} - 167 q^{5} - 299 q^{6} - 9 q^{7} + 262 q^{8} + 300 q^{9} + O(q^{10}) \) \( 2360 q - 9 q^{2} - 20 q^{3} + 1847 q^{4} - 167 q^{5} - 299 q^{6} - 9 q^{7} + 262 q^{8} + 300 q^{9} - 164 q^{10} - 977 q^{11} - 1482 q^{12} - 9 q^{13} - 1785 q^{14} - 5194 q^{15} + 28727 q^{16} + 4588 q^{17} - 11535 q^{18} - 36 q^{19} - 12553 q^{20} + 273 q^{21} - 148 q^{22} - 5681 q^{23} - 33820 q^{24} + 72047 q^{25} + 24240 q^{26} - 14225 q^{27} - 4260 q^{28} - 11115 q^{29} - 40464 q^{30} - 4443 q^{31} - 4905 q^{32} - 70580 q^{33} - 12605 q^{34} - 12536 q^{35} + 8279 q^{36} + 19992 q^{37} - 7293 q^{38} - 1048 q^{39} - 33689 q^{40} + 44703 q^{41} + 5740 q^{42} - 9 q^{43} + 73884 q^{44} - 81452 q^{45} - 46004 q^{46} + 34068 q^{47} + 81664 q^{48} + 238027 q^{49} + 51207 q^{50} - 73810 q^{51} + 18900 q^{52} + 98412 q^{53} + 77640 q^{54} + 15052 q^{55} + 128029 q^{56} - 155367 q^{57} - 3386 q^{58} - 268623 q^{59} - 545822 q^{60} - 46749 q^{61} - 243926 q^{62} - 75137 q^{63} - 911710 q^{64} - 276798 q^{65} + 298823 q^{66} - 5523 q^{67} + 1463882 q^{68} + 376485 q^{69} - 52042 q^{70} + 107582 q^{71} + 385148 q^{72} - 36 q^{73} + 8955 q^{74} + 118735 q^{75} + 52251 q^{76} - 594389 q^{77} - 1354909 q^{78} - 9 q^{79} - 732536 q^{80} + 1151064 q^{81} + 151054 q^{82} - 32996 q^{83} + 179298 q^{84} + 6241 q^{85} + 1248955 q^{86} + 560224 q^{87} + 84023 q^{88} + 351476 q^{89} - 2952536 q^{90} - 67308 q^{91} - 32477 q^{92} + 877560 q^{93} - 188022 q^{94} - 254931 q^{95} - 321054 q^{96} - 238446 q^{97} + 57156 q^{98} + 913028 q^{99} + O(q^{100}) \)

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

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