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Properties

Label 45.10
Level 45
Weight 10
Dimension 457
Nonzero newspaces 6
Newform subspaces 17
Sturm bound 1440
Trace bound 1

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Defining parameters

Level: \( N \) = \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 17 \)
Sturm bound: \(1440\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(45))\).

Total New Old
Modular forms 680 483 197
Cusp forms 616 457 159
Eisenstein series 64 26 38

Trace form

\( 457 q - 88 q^{2} - 2 q^{3} + 2642 q^{4} - 1536 q^{5} - 4894 q^{6} + 22488 q^{7} - 24336 q^{8} - 8926 q^{9} + O(q^{10}) \) \( 457 q - 88 q^{2} - 2 q^{3} + 2642 q^{4} - 1536 q^{5} - 4894 q^{6} + 22488 q^{7} - 24336 q^{8} - 8926 q^{9} + 113846 q^{10} - 188644 q^{11} + 179312 q^{12} + 82664 q^{13} + 192012 q^{14} - 482099 q^{15} + 577290 q^{16} + 122558 q^{17} + 1528336 q^{18} + 677272 q^{19} + 3650500 q^{20} - 2080002 q^{21} - 1577450 q^{22} + 1837152 q^{23} + 7579914 q^{24} - 17386994 q^{25} - 16093564 q^{26} + 10126816 q^{27} + 24461848 q^{28} + 29665264 q^{29} - 8581912 q^{30} - 26040998 q^{31} - 59931602 q^{32} - 6375568 q^{33} - 21044242 q^{34} + 39110416 q^{35} + 45514666 q^{36} + 76226434 q^{37} - 24517450 q^{38} - 93468662 q^{39} - 217671420 q^{40} - 149667386 q^{41} - 45485664 q^{42} + 146578886 q^{43} + 529176820 q^{44} + 18901019 q^{45} + 155799704 q^{46} - 465144928 q^{47} - 331251814 q^{48} - 212728589 q^{49} + 406863470 q^{50} + 174938414 q^{51} + 563961808 q^{52} + 510071426 q^{53} + 212209922 q^{54} - 305009574 q^{55} - 851713812 q^{56} - 479228714 q^{57} - 195878888 q^{58} - 58219012 q^{59} + 639842432 q^{60} + 213848016 q^{61} + 1421788764 q^{62} + 1229848410 q^{63} + 872981388 q^{64} - 1274140249 q^{65} - 4669726268 q^{66} - 1699199934 q^{67} - 2746582802 q^{68} + 1846341378 q^{69} + 1561139034 q^{70} + 3521854804 q^{71} + 3121962858 q^{72} - 1669881346 q^{73} + 1339446676 q^{74} + 819681409 q^{75} + 1990291206 q^{76} - 3038288262 q^{77} - 5941861036 q^{78} + 1039418174 q^{79} - 1076637608 q^{80} + 2083342130 q^{81} - 3862183488 q^{82} - 926051112 q^{83} + 4830712476 q^{84} + 1571050376 q^{85} + 3487645214 q^{86} - 3635090618 q^{87} - 1176819690 q^{88} - 320139066 q^{89} - 9438177692 q^{90} + 2860132416 q^{91} + 6132351516 q^{92} + 6817923414 q^{93} + 3806416532 q^{94} + 2049376916 q^{95} + 5158612576 q^{96} - 11019950462 q^{97} - 12074509538 q^{98} - 4109380118 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(45))\)

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
45.10.a \(\chi_{45}(1, \cdot)\) 45.10.a.a 1 1
45.10.a.b 1
45.10.a.c 1
45.10.a.d 2
45.10.a.e 2
45.10.a.f 2
45.10.a.g 3
45.10.a.h 3
45.10.b \(\chi_{45}(19, \cdot)\) 45.10.b.a 2 1
45.10.b.b 4
45.10.b.c 8
45.10.b.d 8
45.10.e \(\chi_{45}(16, \cdot)\) 45.10.e.a 34 2
45.10.e.b 38
45.10.f \(\chi_{45}(8, \cdot)\) 45.10.f.a 36 2
45.10.j \(\chi_{45}(4, \cdot)\) 45.10.j.a 104 2
45.10.l \(\chi_{45}(2, \cdot)\) 45.10.l.a 208 4

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(45)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 1}\)