Properties

Label 567.3
Level 567
Weight 3
Dimension 17384
Nonzero newspaces 22
Sturm bound 69984
Trace bound 21

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Defining parameters

Level: \( N \) = \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 22 \)
Sturm bound: \(69984\)
Trace bound: \(21\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(567))\).

Total New Old
Modular forms 23976 17944 6032
Cusp forms 22680 17384 5296
Eisenstein series 1296 560 736

Trace form

\( 17384 q - 48 q^{2} - 72 q^{3} - 88 q^{4} - 66 q^{5} - 72 q^{6} - 103 q^{7} - 126 q^{8} - 72 q^{9} + O(q^{10}) \) \( 17384 q - 48 q^{2} - 72 q^{3} - 88 q^{4} - 66 q^{5} - 72 q^{6} - 103 q^{7} - 126 q^{8} - 72 q^{9} - 108 q^{10} - 48 q^{11} - 72 q^{12} - 98 q^{13} - 69 q^{14} - 180 q^{15} - 16 q^{16} - 54 q^{17} + 72 q^{18} + 76 q^{19} + 822 q^{20} + 45 q^{21} + 72 q^{22} + 366 q^{23} + 144 q^{24} + 8 q^{25} - 18 q^{26} - 126 q^{27} - 301 q^{28} - 606 q^{29} - 504 q^{30} - 386 q^{31} - 1404 q^{32} - 450 q^{33} - 516 q^{34} - 549 q^{35} - 900 q^{36} - 392 q^{37} - 420 q^{38} - 72 q^{39} + 114 q^{40} + 852 q^{41} + 405 q^{42} + 388 q^{43} + 2538 q^{44} + 792 q^{45} + 1188 q^{46} + 1410 q^{47} + 918 q^{48} + 323 q^{49} + 2064 q^{50} + 180 q^{51} + 934 q^{52} + 792 q^{53} - 324 q^{54} - 36 q^{55} + 219 q^{56} - 612 q^{57} - 582 q^{58} - 1470 q^{59} - 1710 q^{60} - 1076 q^{61} - 3600 q^{62} - 630 q^{63} - 2302 q^{64} - 3612 q^{65} - 3960 q^{66} - 494 q^{67} - 5508 q^{68} - 2232 q^{69} - 801 q^{70} - 1422 q^{71} - 3528 q^{72} - 806 q^{73} - 2418 q^{74} - 972 q^{75} - 596 q^{76} - 1095 q^{77} - 594 q^{78} - 176 q^{79} - 1224 q^{80} + 72 q^{81} - 492 q^{82} + 330 q^{83} + 837 q^{84} - 222 q^{85} + 1176 q^{86} + 1944 q^{87} - 408 q^{88} + 2700 q^{89} + 4950 q^{90} + 718 q^{91} + 7770 q^{92} + 4320 q^{93} + 534 q^{94} + 6078 q^{95} + 6534 q^{96} + 616 q^{97} + 3663 q^{98} + 2916 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(567))\)

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

Label \(\chi\) Newforms Dimension \(\chi\) degree
567.3.b \(\chi_{567}(323, \cdot)\) 567.3.b.a 24 1
567.3.b.b 24
567.3.d \(\chi_{567}(244, \cdot)\) 567.3.d.a 2 1
567.3.d.b 2
567.3.d.c 4
567.3.d.d 6
567.3.d.e 6
567.3.d.f 12
567.3.d.g 14
567.3.d.h 14
567.3.j \(\chi_{567}(296, \cdot)\) n/a 124 2
567.3.k \(\chi_{567}(460, \cdot)\) n/a 124 2
567.3.l \(\chi_{567}(55, \cdot)\) n/a 124 2
567.3.m \(\chi_{567}(82, \cdot)\) n/a 120 2
567.3.n \(\chi_{567}(53, \cdot)\) n/a 124 2
567.3.q \(\chi_{567}(242, \cdot)\) n/a 120 2
567.3.r \(\chi_{567}(134, \cdot)\) 567.3.r.a 8 2
567.3.r.b 8
567.3.r.c 8
567.3.r.d 8
567.3.r.e 16
567.3.r.f 48
567.3.t \(\chi_{567}(136, \cdot)\) n/a 124 2
567.3.x \(\chi_{567}(73, \cdot)\) n/a 276 6
567.3.y \(\chi_{567}(118, \cdot)\) n/a 276 6
567.3.z \(\chi_{567}(10, \cdot)\) n/a 276 6
567.3.bb \(\chi_{567}(8, \cdot)\) n/a 216 6
567.3.bc \(\chi_{567}(170, \cdot)\) n/a 276 6
567.3.bf \(\chi_{567}(44, \cdot)\) n/a 276 6
567.3.bj \(\chi_{567}(11, \cdot)\) n/a 2556 18
567.3.bk \(\chi_{567}(40, \cdot)\) n/a 2556 18
567.3.bn \(\chi_{567}(13, \cdot)\) n/a 2556 18
567.3.bo \(\chi_{567}(31, \cdot)\) n/a 2556 18
567.3.bp \(\chi_{567}(29, \cdot)\) n/a 1944 18
567.3.bq \(\chi_{567}(2, \cdot)\) n/a 2556 18

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(567))\) into lower level spaces

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