Properties

Label 570.6
Level 570
Weight 6
Dimension 9844
Nonzero newspaces 18
Sturm bound 103680
Trace bound 7

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Defining parameters

Level: \( N \) = \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(103680\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(570))\).

Total New Old
Modular forms 43776 9844 33932
Cusp forms 42624 9844 32780
Eisenstein series 1152 0 1152

Trace form

\( 9844q - 28q^{3} + 128q^{4} + 208q^{5} - 304q^{6} - 544q^{7} + 648q^{9} + O(q^{10}) \) \( 9844q - 28q^{3} + 128q^{4} + 208q^{5} - 304q^{6} - 544q^{7} + 648q^{9} + 736q^{10} - 160q^{11} + 1024q^{12} - 23744q^{13} - 13024q^{14} - 9424q^{15} + 6144q^{16} + 23496q^{17} + 4544q^{18} + 49016q^{19} + 3008q^{20} - 10036q^{21} - 27536q^{22} - 29064q^{23} + 2304q^{24} - 9408q^{25} - 14688q^{26} + 20042q^{27} + 48512q^{28} - 51384q^{29} - 18768q^{30} - 162840q^{31} - 23620q^{33} + 38016q^{34} + 140264q^{35} + 5504q^{36} + 209800q^{37} + 5664q^{38} + 139140q^{39} - 7680q^{40} - 52216q^{41} - 84224q^{42} - 330224q^{43} - 44288q^{44} - 234572q^{45} - 102400q^{46} - 161016q^{47} + 39424q^{48} + 227328q^{49} + 42304q^{50} + 673486q^{51} + 67072q^{52} + 3936q^{53} - 235008q^{54} + 213792q^{55} - 11264q^{56} - 715628q^{57} - 7168q^{58} - 195280q^{59} - 79744q^{60} - 349784q^{61} - 34752q^{62} + 793148q^{63} + 32768q^{64} + 90324q^{65} + 1054976q^{66} - 313936q^{67} + 100608q^{68} + 592092q^{69} + 177408q^{70} + 122568q^{71} - 350336q^{72} - 472116q^{73} - 619456q^{74} - 860480q^{75} - 19968q^{76} - 1509168q^{77} - 731328q^{78} + 409672q^{79} + 53248q^{80} + 1315624q^{81} + 1718464q^{82} + 1407984q^{83} + 891072q^{84} + 3189664q^{85} + 979456q^{86} - 225808q^{87} + 105472q^{88} - 857360q^{89} - 875800q^{90} - 1942528q^{91} - 869376q^{92} - 1632676q^{93} - 2893440q^{94} - 2799084q^{95} + 4096q^{96} - 828200q^{97} - 1277952q^{98} + 170874q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(570))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
570.6.a \(\chi_{570}(1, \cdot)\) 570.6.a.a 1 1
570.6.a.b 2
570.6.a.c 2
570.6.a.d 3
570.6.a.e 3
570.6.a.f 3
570.6.a.g 3
570.6.a.h 4
570.6.a.i 4
570.6.a.j 4
570.6.a.k 4
570.6.a.l 4
570.6.a.m 4
570.6.a.n 4
570.6.a.o 5
570.6.a.p 5
570.6.a.q 5
570.6.c \(\chi_{570}(569, \cdot)\) n/a 200 1
570.6.d \(\chi_{570}(229, \cdot)\) 570.6.d.a 18 1
570.6.d.b 22
570.6.d.c 24
570.6.d.d 24
570.6.f \(\chi_{570}(341, \cdot)\) n/a 136 1
570.6.i \(\chi_{570}(121, \cdot)\) n/a 128 2
570.6.k \(\chi_{570}(77, \cdot)\) n/a 360 2
570.6.m \(\chi_{570}(37, \cdot)\) n/a 200 2
570.6.n \(\chi_{570}(179, \cdot)\) n/a 400 2
570.6.q \(\chi_{570}(49, \cdot)\) n/a 200 2
570.6.s \(\chi_{570}(221, \cdot)\) n/a 272 2
570.6.u \(\chi_{570}(61, \cdot)\) n/a 408 6
570.6.v \(\chi_{570}(83, \cdot)\) n/a 800 4
570.6.x \(\chi_{570}(103, \cdot)\) n/a 400 4
570.6.bb \(\chi_{570}(41, \cdot)\) n/a 792 6
570.6.bc \(\chi_{570}(139, \cdot)\) n/a 600 6
570.6.bf \(\chi_{570}(29, \cdot)\) n/a 1200 6
570.6.bh \(\chi_{570}(13, \cdot)\) n/a 1200 12
570.6.bi \(\chi_{570}(17, \cdot)\) n/a 2400 12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(570))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(570)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 2}\)