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Properties

Label 567.4
Level 567
Weight 4
Dimension 26216
Nonzero newspaces 22
Sturm bound 93312
Trace bound 21

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Defining parameters

Level: \( N \) = \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 22 \)
Sturm bound: \(93312\)
Trace bound: \(21\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(567))\).

Total New Old
Modular forms 35640 26776 8864
Cusp forms 34344 26216 8128
Eisenstein series 1296 560 736

Trace form

\( 26216 q - 48 q^{2} - 72 q^{3} - 64 q^{4} - 24 q^{5} - 72 q^{6} - 118 q^{7} - 258 q^{8} - 72 q^{9} + O(q^{10}) \) \( 26216 q - 48 q^{2} - 72 q^{3} - 64 q^{4} - 24 q^{5} - 72 q^{6} - 118 q^{7} - 258 q^{8} - 72 q^{9} - 156 q^{10} + 78 q^{11} - 72 q^{12} + 28 q^{13} - 3 q^{14} - 180 q^{15} - 424 q^{16} - 450 q^{17} - 900 q^{18} - 1016 q^{19} - 2382 q^{20} - 198 q^{21} + 156 q^{22} + 1524 q^{23} + 2088 q^{24} + 1646 q^{25} + 6582 q^{26} + 1332 q^{27} + 1403 q^{28} + 1932 q^{29} + 1440 q^{30} - 188 q^{31} - 1764 q^{32} - 936 q^{33} - 1848 q^{34} - 2553 q^{35} - 4788 q^{36} - 3176 q^{37} - 4992 q^{38} - 72 q^{39} - 4194 q^{40} - 7206 q^{41} - 3645 q^{42} - 3098 q^{43} - 9786 q^{44} - 2124 q^{45} + 276 q^{46} + 3120 q^{47} + 4482 q^{48} - 802 q^{49} + 11436 q^{50} + 5850 q^{51} + 4618 q^{52} + 8622 q^{53} + 13284 q^{54} + 8808 q^{55} + 15303 q^{56} + 4248 q^{57} + 11454 q^{58} + 11838 q^{59} + 2502 q^{60} + 3232 q^{61} + 876 q^{62} - 2088 q^{63} - 3118 q^{64} - 3972 q^{65} + 3816 q^{66} - 10718 q^{67} - 10440 q^{68} + 684 q^{69} - 5511 q^{70} - 5598 q^{71} - 3528 q^{72} - 2852 q^{73} - 11454 q^{74} - 9072 q^{75} + 532 q^{76} - 13116 q^{77} - 21978 q^{78} + 3988 q^{79} - 29796 q^{80} - 11592 q^{81} + 828 q^{82} - 3756 q^{83} - 17469 q^{84} + 6618 q^{85} - 7188 q^{86} - 11016 q^{87} - 5712 q^{88} - 24570 q^{89} - 22266 q^{90} - 9881 q^{91} - 38490 q^{92} - 7668 q^{93} - 26778 q^{94} - 12126 q^{95} + 34398 q^{96} - 10430 q^{97} + 16791 q^{98} + 26244 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(567))\)

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
567.4.a \(\chi_{567}(1, \cdot)\) 567.4.a.a 1 1
567.4.a.b 1
567.4.a.c 3
567.4.a.d 3
567.4.a.e 5
567.4.a.f 5
567.4.a.g 8
567.4.a.h 8
567.4.a.i 8
567.4.a.j 9
567.4.a.k 9
567.4.a.l 12
567.4.c \(\chi_{567}(566, \cdot)\) 567.4.c.a 8 1
567.4.c.b 40
567.4.c.c 44
567.4.e \(\chi_{567}(163, \cdot)\) n/a 184 2
567.4.f \(\chi_{567}(190, \cdot)\) n/a 144 2
567.4.g \(\chi_{567}(109, \cdot)\) n/a 188 2
567.4.h \(\chi_{567}(298, \cdot)\) n/a 188 2
567.4.i \(\chi_{567}(215, \cdot)\) n/a 188 2
567.4.o \(\chi_{567}(188, \cdot)\) n/a 188 2
567.4.p \(\chi_{567}(80, \cdot)\) n/a 184 2
567.4.s \(\chi_{567}(26, \cdot)\) n/a 188 2
567.4.u \(\chi_{567}(100, \cdot)\) n/a 420 6
567.4.v \(\chi_{567}(64, \cdot)\) n/a 324 6
567.4.w \(\chi_{567}(37, \cdot)\) n/a 420 6
567.4.ba \(\chi_{567}(143, \cdot)\) n/a 420 6
567.4.bd \(\chi_{567}(17, \cdot)\) n/a 420 6
567.4.be \(\chi_{567}(62, \cdot)\) n/a 420 6
567.4.bg \(\chi_{567}(4, \cdot)\) n/a 3852 18
567.4.bh \(\chi_{567}(22, \cdot)\) n/a 2916 18
567.4.bi \(\chi_{567}(25, \cdot)\) n/a 3852 18
567.4.bl \(\chi_{567}(47, \cdot)\) n/a 3852 18
567.4.bm \(\chi_{567}(20, \cdot)\) n/a 3852 18
567.4.br \(\chi_{567}(5, \cdot)\) n/a 3852 18

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(567))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(567)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 2}\)