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Properties

Label 207.6
Level 207
Weight 6
Dimension 6153
Nonzero newspaces 8
Sturm bound 19008
Trace bound 2

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Defining parameters

Level: \( N \) = \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(19008\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(207))\).

Total New Old
Modular forms 8096 6341 1755
Cusp forms 7744 6153 1591
Eisenstein series 352 188 164

Trace form

\( 6153 q - 51 q^{2} - 20 q^{3} + 57 q^{4} - 177 q^{5} - 386 q^{6} - 9 q^{7} + 1803 q^{8} + 784 q^{9} + O(q^{10}) \) \( 6153 q - 51 q^{2} - 20 q^{3} + 57 q^{4} - 177 q^{5} - 386 q^{6} - 9 q^{7} + 1803 q^{8} + 784 q^{9} - 147 q^{10} - 2049 q^{11} - 5492 q^{12} - 945 q^{13} - 2337 q^{14} + 4060 q^{15} + 6689 q^{16} + 14414 q^{17} + 16156 q^{18} - 110 q^{19} - 21097 q^{20} - 17384 q^{21} - 19482 q^{22} - 19859 q^{23} - 1186 q^{24} + 8771 q^{25} + 49039 q^{26} + 20260 q^{27} + 44965 q^{28} - 3562 q^{29} - 44252 q^{30} - 10976 q^{31} - 45887 q^{32} + 17596 q^{33} - 85709 q^{34} + 15985 q^{35} + 29134 q^{36} + 107189 q^{37} + 124684 q^{38} - 16484 q^{39} + 83623 q^{40} - 15587 q^{41} - 20240 q^{42} - 66493 q^{43} - 241534 q^{44} - 86120 q^{45} - 225251 q^{46} - 110374 q^{47} + 114766 q^{48} - 7929 q^{49} + 199274 q^{50} + 18748 q^{51} + 339173 q^{52} + 97525 q^{53} + 405114 q^{54} + 476075 q^{55} + 185812 q^{56} + 23686 q^{57} - 632330 q^{58} - 765803 q^{59} - 1017940 q^{60} - 551373 q^{61} - 844449 q^{62} - 281502 q^{63} + 324249 q^{64} + 623196 q^{65} + 832032 q^{66} + 343473 q^{67} + 2084418 q^{68} + 626988 q^{69} + 1074426 q^{70} + 664008 q^{71} + 452830 q^{72} - 131169 q^{73} - 245782 q^{74} - 424426 q^{75} - 1423078 q^{76} - 1019482 q^{77} - 1328600 q^{78} - 639137 q^{79} - 1920708 q^{80} - 912328 q^{81} + 416931 q^{82} + 294734 q^{83} + 849808 q^{84} + 1129567 q^{85} + 1642739 q^{86} + 285868 q^{87} - 510351 q^{88} + 261897 q^{89} + 1080444 q^{90} - 900582 q^{91} - 948138 q^{92} - 227884 q^{93} - 1194898 q^{94} - 1413000 q^{95} - 63052 q^{96} - 473406 q^{97} + 283887 q^{98} - 67436 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(207))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
207.6.a \(\chi_{207}(1, \cdot)\) 207.6.a.a 2 1
207.6.a.b 3
207.6.a.c 3
207.6.a.d 4
207.6.a.e 4
207.6.a.f 5
207.6.a.g 6
207.6.a.h 10
207.6.a.i 10
207.6.c \(\chi_{207}(206, \cdot)\) 207.6.c.a 40 1
207.6.e \(\chi_{207}(70, \cdot)\) n/a 220 2
207.6.g \(\chi_{207}(68, \cdot)\) n/a 236 2
207.6.i \(\chi_{207}(55, \cdot)\) n/a 490 10
207.6.k \(\chi_{207}(17, \cdot)\) n/a 400 10
207.6.m \(\chi_{207}(4, \cdot)\) n/a 2360 20
207.6.o \(\chi_{207}(5, \cdot)\) n/a 2360 20

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(207))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(207)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)