Properties

Label 45.6
Level 45
Weight 6
Dimension 249
Nonzero newspaces 6
Newform subspaces 15
Sturm bound 864
Trace bound 1

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 15 \)
Sturm bound: \(864\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(45))\).

Total New Old
Modular forms 392 275 117
Cusp forms 328 249 79
Eisenstein series 64 26 38

Trace form

\( 249q - 20q^{2} + 16q^{3} + 34q^{4} - 141q^{5} - 358q^{6} + 212q^{7} + 1968q^{8} + 944q^{9} + O(q^{10}) \) \( 249q - 20q^{2} + 16q^{3} + 34q^{4} - 141q^{5} - 358q^{6} + 212q^{7} + 1968q^{8} + 944q^{9} - 2414q^{10} - 3188q^{11} - 5200q^{12} + 1466q^{13} + 5148q^{14} + 4216q^{15} + 3530q^{16} + 6658q^{17} + 11776q^{18} - 7212q^{19} - 12940q^{20} - 15276q^{21} - 14562q^{22} - 25476q^{23} - 13782q^{24} - 12369q^{25} + 47788q^{26} + 30400q^{27} + 43256q^{28} + 8342q^{29} + 10328q^{30} + 19344q^{31} + 6062q^{32} - 18112q^{33} - 45442q^{34} - 27064q^{35} + 51082q^{36} - 57166q^{37} - 4754q^{38} + 11848q^{39} + 49460q^{40} + 38762q^{41} - 69792q^{42} + 19184q^{43} - 166540q^{44} - 106186q^{45} + 65144q^{46} + 14776q^{47} + 82010q^{48} - 61963q^{49} - 51230q^{50} - 424q^{51} - 227632q^{52} - 9902q^{53} + 114794q^{54} - 1044q^{55} + 316716q^{56} + 262612q^{57} + 400176q^{58} + 281644q^{59} + 162512q^{60} + 80778q^{61} - 376644q^{62} - 294588q^{63} - 376308q^{64} - 312224q^{65} - 165500q^{66} - 247144q^{67} - 395506q^{68} + 20304q^{69} - 356406q^{70} + 152384q^{71} - 200598q^{72} + 119894q^{73} + 774908q^{74} + 373864q^{75} + 910502q^{76} + 534840q^{77} + 561476q^{78} - 122580q^{79} + 315032q^{80} - 193660q^{81} - 89784q^{82} - 398880q^{83} - 782340q^{84} - 127514q^{85} - 857450q^{86} - 208052q^{87} + 512598q^{88} + 294138q^{89} - 746972q^{90} + 214960q^{91} - 1054404q^{92} - 793296q^{93} - 853756q^{94} - 709304q^{95} + 49216q^{96} - 690094q^{97} + 853658q^{98} + 1056748q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)

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
45.6.a \(\chi_{45}(1, \cdot)\) 45.6.a.a 1 1
45.6.a.b 1
45.6.a.c 1
45.6.a.d 2
45.6.a.e 2
45.6.a.f 2
45.6.b \(\chi_{45}(19, \cdot)\) 45.6.b.a 2 1
45.6.b.b 2
45.6.b.c 4
45.6.b.d 4
45.6.e \(\chi_{45}(16, \cdot)\) 45.6.e.a 18 2
45.6.e.b 22
45.6.f \(\chi_{45}(8, \cdot)\) 45.6.f.a 20 2
45.6.j \(\chi_{45}(4, \cdot)\) 45.6.j.a 56 2
45.6.l \(\chi_{45}(2, \cdot)\) 45.6.l.a 112 4

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(45)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)