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Properties

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

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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

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

Display 100 coefficients 10 coefficients

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 available 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

\( S_{6}^{\mathrm{old}}(\Gamma_1(45)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 1}\)