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Properties

Label 531.5
Level 531
Weight 5
Dimension 32783
Nonzero newspaces 8
Sturm bound 104400
Trace bound 2

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Defining parameters

Level: \( N \) = \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(104400\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(531))\).

Total New Old
Modular forms 42224 33297 8927
Cusp forms 41296 32783 8513
Eisenstein series 928 514 414

Trace form

\( 32783 q - 81 q^{2} - 110 q^{3} - 109 q^{4} - 63 q^{5} + 82 q^{6} + q^{7} - 87 q^{8} - 314 q^{9} + O(q^{10}) \) \( 32783 q - 81 q^{2} - 110 q^{3} - 109 q^{4} - 63 q^{5} + 82 q^{6} + q^{7} - 87 q^{8} - 314 q^{9} - 693 q^{10} - 1053 q^{11} - 776 q^{12} + 373 q^{13} + 2205 q^{14} + 1936 q^{15} + 1019 q^{16} - 87 q^{17} - 2924 q^{18} - 1985 q^{19} - 3315 q^{20} - 1076 q^{21} + 939 q^{22} + 477 q^{23} + 2782 q^{24} + 1487 q^{25} - 87 q^{26} - 224 q^{27} - 3101 q^{28} + 2025 q^{29} + 2440 q^{30} - 1211 q^{31} + 2235 q^{32} - 674 q^{33} - 2625 q^{34} - 87 q^{35} + 4654 q^{36} + 3019 q^{37} + 1491 q^{38} - 4064 q^{39} - 4515 q^{40} - 15345 q^{41} - 19340 q^{42} - 6461 q^{43} - 87 q^{44} + 8308 q^{45} + 60987 q^{46} + 27810 q^{47} + 13426 q^{48} + 1233 q^{49} - 39549 q^{50} - 5030 q^{51} - 47831 q^{52} - 23577 q^{53} + 694 q^{54} - 32670 q^{55} - 49275 q^{56} - 10850 q^{57} - 29758 q^{58} + 474 q^{59} - 15172 q^{60} + 1843 q^{61} + 24969 q^{62} + 15040 q^{63} + 110759 q^{64} + 63558 q^{65} + 27352 q^{66} + 52825 q^{67} + 62679 q^{68} + 27640 q^{69} + 27825 q^{70} - 20445 q^{71} - 17018 q^{72} - 31814 q^{73} - 153219 q^{74} - 42158 q^{75} + 12487 q^{76} - 5247 q^{77} + 24004 q^{78} + 7489 q^{79} - 87 q^{80} - 36890 q^{81} - 11601 q^{82} + 3645 q^{83} + 12856 q^{84} - 14235 q^{85} + 75375 q^{86} + 43012 q^{87} - 25629 q^{88} - 87 q^{89} - 41696 q^{90} - 82477 q^{91} - 67359 q^{92} - 38624 q^{93} + 3153 q^{94} + 26637 q^{95} + 7228 q^{96} + 81127 q^{97} + 272658 q^{98} + 18136 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(531))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
531.5.b \(\chi_{531}(296, \cdot)\) 531.5.b.a 76 1
531.5.c \(\chi_{531}(235, \cdot)\) 531.5.c.a 3 1
531.5.c.b 16
531.5.c.c 40
531.5.c.d 40
531.5.g \(\chi_{531}(58, \cdot)\) n/a 476 2
531.5.h \(\chi_{531}(119, \cdot)\) n/a 464 2
531.5.k \(\chi_{531}(10, \cdot)\) n/a 2772 28
531.5.l \(\chi_{531}(17, \cdot)\) n/a 2240 28
531.5.n \(\chi_{531}(5, \cdot)\) n/a 13328 56
531.5.o \(\chi_{531}(13, \cdot)\) n/a 13328 56

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(531))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(531)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 2}\)