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Properties

Label 531.4
Level 531
Weight 4
Dimension 24524
Nonzero newspaces 8
Sturm bound 83520
Trace bound 2

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Defining parameters

Level: \( N \) = \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(83520\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(531))\).

Total New Old
Modular forms 31784 25036 6748
Cusp forms 30856 24524 6332
Eisenstein series 928 512 416

Trace form

\( 24524 q - 81 q^{2} - 110 q^{3} - 61 q^{4} - 57 q^{5} - 134 q^{6} - 113 q^{7} - 219 q^{8} - 206 q^{9} + O(q^{10}) \) \( 24524 q - 81 q^{2} - 110 q^{3} - 61 q^{4} - 57 q^{5} - 134 q^{6} - 113 q^{7} - 219 q^{8} - 206 q^{9} - 285 q^{10} + 45 q^{11} + 196 q^{12} + 31 q^{13} + 33 q^{14} - 170 q^{15} - 229 q^{16} - 483 q^{17} - 548 q^{18} - 65 q^{19} - 111 q^{20} - 158 q^{21} - 153 q^{22} - 21 q^{23} + 82 q^{24} - 79 q^{25} + 969 q^{26} + 748 q^{27} - 605 q^{28} - 189 q^{29} - 692 q^{30} - 617 q^{31} - 933 q^{32} - 512 q^{33} + 507 q^{34} - 99 q^{35} + 334 q^{36} - 281 q^{37} - 1209 q^{38} - 1634 q^{39} + 441 q^{40} + 177 q^{41} + 856 q^{42} + 1129 q^{43} + 837 q^{44} + 1234 q^{45} - 4889 q^{46} - 1435 q^{47} - 74 q^{48} - 3083 q^{49} - 2569 q^{50} - 710 q^{51} - 891 q^{52} + 1321 q^{53} - 2546 q^{54} + 1233 q^{55} + 12109 q^{56} + 2326 q^{57} + 3128 q^{58} + 4075 q^{59} - 160 q^{60} + 3443 q^{61} + 2125 q^{62} - 1322 q^{63} + 10167 q^{64} + 1635 q^{65} + 1864 q^{66} + 2837 q^{67} - 2413 q^{68} - 1898 q^{69} - 8035 q^{70} - 11243 q^{71} - 1898 q^{72} - 5229 q^{73} - 9011 q^{74} + 610 q^{75} - 2249 q^{76} - 417 q^{77} + 1864 q^{78} - 3461 q^{79} - 471 q^{80} + 1018 q^{81} - 7521 q^{82} + 1539 q^{83} - 1400 q^{84} + 1101 q^{85} - 21 q^{86} + 190 q^{87} + 2355 q^{88} + 1497 q^{89} + 1396 q^{90} + 5663 q^{91} - 1803 q^{92} + 310 q^{93} + 4113 q^{94} - 351 q^{95} - 2276 q^{96} + 4045 q^{97} - 21276 q^{98} - 710 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(531))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
531.4.a \(\chi_{531}(1, \cdot)\) 531.4.a.a 2 1
531.4.a.b 2
531.4.a.c 7
531.4.a.d 7
531.4.a.e 8
531.4.a.f 8
531.4.a.g 10
531.4.a.h 14
531.4.a.i 14
531.4.d \(\chi_{531}(530, \cdot)\) 531.4.d.a 60 1
531.4.e \(\chi_{531}(178, \cdot)\) n/a 348 2
531.4.f \(\chi_{531}(176, \cdot)\) n/a 356 2
531.4.i \(\chi_{531}(19, \cdot)\) n/a 2072 28
531.4.j \(\chi_{531}(8, \cdot)\) n/a 1680 28
531.4.m \(\chi_{531}(4, \cdot)\) n/a 9968 56
531.4.p \(\chi_{531}(2, \cdot)\) n/a 9968 56

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(531))\) into lower level spaces

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