Properties

Label 531.8
Level 531
Weight 8
Dimension 57564
Nonzero newspaces 8
Sturm bound 167040
Trace bound 2

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Defining parameters

Level: \( N \) = \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(167040\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(531))\).

Total New Old
Modular forms 73544 58076 15468
Cusp forms 72616 57564 15052
Eisenstein series 928 512 416

Trace form

\( 57564q - 57q^{2} - 164q^{3} - 189q^{4} + 1053q^{5} + 2350q^{6} - 831q^{7} - 14571q^{8} - 2096q^{9} + O(q^{10}) \) \( 57564q - 57q^{2} - 164q^{3} - 189q^{4} + 1053q^{5} + 2350q^{6} - 831q^{7} - 14571q^{8} - 2096q^{9} + 17595q^{10} + 14937q^{11} - 16220q^{12} - 13755q^{13} + 31689q^{14} + 2260q^{15} - 13941q^{16} - 4443q^{17} - 85868q^{18} - 164589q^{19} + 9729q^{20} + 374332q^{21} + 542091q^{22} + 72513q^{23} - 431054q^{24} - 213669q^{25} - 1134207q^{26} - 644660q^{27} - 404349q^{28} + 902229q^{29} + 2224108q^{30} + 531105q^{31} + 2482059q^{32} + 296920q^{33} - 1924593q^{34} - 4471239q^{35} - 5003738q^{36} + 707079q^{37} + 3801843q^{38} + 4114516q^{39} + 2814681q^{40} + 2203641q^{41} - 1077848q^{42} - 2218935q^{43} - 10163883q^{44} - 5375276q^{45} + 4194715q^{46} + 9335200q^{47} + 14868934q^{48} + 6573085q^{49} - 4288169q^{50} - 5051492q^{51} - 26460859q^{52} - 13630933q^{53} - 11633174q^{54} - 4463832q^{55} + 28043981q^{56} + 6143584q^{57} + 23258228q^{58} + 14079575q^{59} - 743200q^{60} + 11701747q^{61} - 4483183q^{62} + 4477492q^{63} - 62742281q^{64} - 27723150q^{65} - 11509640q^{66} - 34463177q^{67} - 16464677q^{68} + 6004468q^{69} + 48580805q^{70} + 38707991q^{71} + 19276534q^{72} + 34809242q^{73} - 47489647q^{74} - 38349380q^{75} - 18917841q^{76} - 6836391q^{77} + 26679808q^{78} - 9013215q^{79} + 79152489q^{80} + 57077344q^{81} - 17931249q^{82} - 27963687q^{83} - 60180296q^{84} + 10010001q^{85} - 60327945q^{86} - 20581532q^{87} + 78338451q^{88} + 32203821q^{89} + 27321076q^{90} - 34958613q^{91} - 75473883q^{92} - 54662540q^{93} - 75151815q^{94} - 27567831q^{95} + 6808636q^{96} + 49529049q^{97} - 83487504q^{98} + 98765236q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(531))\)

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
531.8.a \(\chi_{531}(1, \cdot)\) 531.8.a.a 14 1
531.8.a.b 16
531.8.a.c 17
531.8.a.d 17
531.8.a.e 18
531.8.a.f 20
531.8.a.g 33
531.8.a.h 33
531.8.d \(\chi_{531}(530, \cdot)\) n/a 140 1
531.8.e \(\chi_{531}(178, \cdot)\) n/a 812 2
531.8.f \(\chi_{531}(176, \cdot)\) n/a 836 2
531.8.i \(\chi_{531}(19, \cdot)\) n/a 4872 28
531.8.j \(\chi_{531}(8, \cdot)\) n/a 3920 28
531.8.m \(\chi_{531}(4, \cdot)\) n/a 23408 56
531.8.p \(\chi_{531}(2, \cdot)\) n/a 23408 56

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(531))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(531)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 2}\)