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Properties

Label 531.2
Level 531
Weight 2
Dimension 8004
Nonzero newspaces 8
Newform subspaces 20
Sturm bound 41760
Trace bound 3

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Defining parameters

Level: \( N \) = \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 20 \)
Sturm bound: \(41760\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(531))\).

Total New Old
Modular forms 10904 8516 2388
Cusp forms 9977 8004 1973
Eisenstein series 927 512 415

Trace form

\( 8004 q - 87 q^{2} - 116 q^{3} - 87 q^{4} - 87 q^{5} - 116 q^{6} - 87 q^{7} - 87 q^{8} - 116 q^{9} + O(q^{10}) \) \( 8004 q - 87 q^{2} - 116 q^{3} - 87 q^{4} - 87 q^{5} - 116 q^{6} - 87 q^{7} - 87 q^{8} - 116 q^{9} - 261 q^{10} - 87 q^{11} - 116 q^{12} - 87 q^{13} - 87 q^{14} - 116 q^{15} - 87 q^{16} - 87 q^{17} - 116 q^{18} - 261 q^{19} - 87 q^{20} - 116 q^{21} - 87 q^{22} - 87 q^{23} - 116 q^{24} - 87 q^{25} - 87 q^{26} - 116 q^{27} - 261 q^{28} - 87 q^{29} - 116 q^{30} - 87 q^{31} - 87 q^{32} - 116 q^{33} - 87 q^{34} - 87 q^{35} - 116 q^{36} - 261 q^{37} - 87 q^{38} - 116 q^{39} - 87 q^{40} - 87 q^{41} - 116 q^{42} - 87 q^{43} - 87 q^{44} - 116 q^{45} - 319 q^{46} - 116 q^{47} - 116 q^{48} - 145 q^{49} - 203 q^{50} - 116 q^{51} - 203 q^{52} - 145 q^{53} - 116 q^{54} - 348 q^{55} - 319 q^{56} - 116 q^{57} - 174 q^{58} - 145 q^{59} - 232 q^{60} - 145 q^{61} - 145 q^{62} - 116 q^{63} - 493 q^{64} - 174 q^{65} - 116 q^{66} - 145 q^{67} - 203 q^{68} - 116 q^{69} - 203 q^{70} - 145 q^{71} - 116 q^{72} - 290 q^{73} - 145 q^{74} - 116 q^{75} - 87 q^{76} - 87 q^{77} - 116 q^{78} - 87 q^{79} - 87 q^{80} - 116 q^{81} - 261 q^{82} - 87 q^{83} - 116 q^{84} - 87 q^{85} - 87 q^{86} - 116 q^{87} - 87 q^{88} - 87 q^{89} - 116 q^{90} - 261 q^{91} - 87 q^{92} - 116 q^{93} - 87 q^{94} - 87 q^{95} - 116 q^{96} - 87 q^{97} - 174 q^{98} - 116 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(531))\)

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
531.2.a \(\chi_{531}(1, \cdot)\) 531.2.a.a 2 1
531.2.a.b 2
531.2.a.c 2
531.2.a.d 3
531.2.a.e 5
531.2.a.f 5
531.2.a.g 5
531.2.d \(\chi_{531}(530, \cdot)\) 531.2.d.a 20 1
531.2.e \(\chi_{531}(178, \cdot)\) 531.2.e.a 4 2
531.2.e.b 42
531.2.e.c 70
531.2.f \(\chi_{531}(176, \cdot)\) 531.2.f.a 12 2
531.2.f.b 104
531.2.i \(\chi_{531}(19, \cdot)\) 531.2.i.a 112 28
531.2.i.b 140
531.2.i.c 140
531.2.i.d 280
531.2.j \(\chi_{531}(8, \cdot)\) 531.2.j.a 560 28
531.2.m \(\chi_{531}(4, \cdot)\) 531.2.m.a 3248 56
531.2.p \(\chi_{531}(2, \cdot)\) 531.2.p.a 3248 56

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(531))\) into lower level spaces

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