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Properties

Label 45.18
Level 45
Weight 18
Dimension 875
Nonzero newspaces 6
Sturm bound 2592
Trace bound 1

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Defining parameters

Level: \( N \) = \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(2592\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(45))\).

Total New Old
Modular forms 1256 901 355
Cusp forms 1192 875 317
Eisenstein series 64 26 38

Trace form

\( 875 q - 232 q^{2} + 4552 q^{3} + 1300050 q^{4} - 1318251 q^{5} + 23947778 q^{6} - 15452652 q^{7} + 642671472 q^{8} - 880812568 q^{9} + O(q^{10}) \) \( 875 q - 232 q^{2} + 4552 q^{3} + 1300050 q^{4} - 1318251 q^{5} + 23947778 q^{6} - 15452652 q^{7} + 642671472 q^{8} - 880812568 q^{9} + 2267162566 q^{10} - 3526468564 q^{11} + 3973676528 q^{12} + 2019465978 q^{13} - 10589969268 q^{14} - 1890891104 q^{15} + 36879666442 q^{16} + 5045708042 q^{17} - 65740874864 q^{18} - 72403926596 q^{19} + 487872893380 q^{20} + 138667086276 q^{21} + 836999265078 q^{22} - 966826823988 q^{23} - 2057107039158 q^{24} - 3172147797919 q^{25} + 12294439024868 q^{26} - 17272953588224 q^{27} - 8977194319272 q^{28} + 13305129311506 q^{29} + 2102380425608 q^{30} - 45110573352608 q^{31} + 33196764239278 q^{32} - 27470147018872 q^{33} + 9220022407982 q^{34} - 2258976795224 q^{35} - 188585862535766 q^{36} + 99095407315842 q^{37} + 21161410135574 q^{38} - 45217111855352 q^{39} + 231669439261220 q^{40} - 306390485912162 q^{41} - 422545096771296 q^{42} - 104407924061712 q^{43} + 314482747863028 q^{44} + 9557289696254 q^{45} - 1356694991892712 q^{46} + 340570037799080 q^{47} + 1011164122614170 q^{48} + 1784155394915699 q^{49} - 171520562320930 q^{50} - 3221170314215536 q^{51} - 1460498125429488 q^{52} + 4746529858482482 q^{53} + 631919508088418 q^{54} - 1931584507059084 q^{55} - 1388473079340948 q^{56} - 793787735858084 q^{57} + 4748322320985336 q^{58} + 4083568950539852 q^{59} + 7869281467880672 q^{60} - 11161653506873714 q^{61} + 5955784574833884 q^{62} - 3779529069144780 q^{63} + 6039622623359372 q^{64} + 10248404168680376 q^{65} - 29739068715868604 q^{66} - 5694238900041336 q^{67} + 11641795946223790 q^{68} + 5869832068000656 q^{69} + 35796583116498714 q^{70} - 76193681771496656 q^{71} - 49139462176442646 q^{72} + 23033415465943278 q^{73} + 126193226994198964 q^{74} + 60438361141079824 q^{75} - 133515208243255674 q^{76} - 142622840860995672 q^{77} + 69575225579153300 q^{78} + 24702651898403980 q^{79} + 231669905183889112 q^{80} - 15929787361627060 q^{81} - 38209247404889760 q^{82} - 237482350806103272 q^{83} - 320728072199429796 q^{84} - 133786288298702594 q^{85} + 551184909149137598 q^{86} + 333906427273146796 q^{87} + 134677394308026390 q^{88} - 768463887602271666 q^{89} - 263876837546207132 q^{90} + 6204379858779120 q^{91} + 699440982407855964 q^{92} + 434619633044432880 q^{93} + 31419690464796308 q^{94} - 355696843098845944 q^{95} - 1156478104165596512 q^{96} + 203198496495346242 q^{97} + 1998398322917823982 q^{98} + 1010214492419503804 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(45))\)

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
45.18.a \(\chi_{45}(1, \cdot)\) 45.18.a.a 2 1
45.18.a.b 2
45.18.a.c 3
45.18.a.d 3
45.18.a.e 3
45.18.a.f 4
45.18.a.g 6
45.18.a.h 6
45.18.b \(\chi_{45}(19, \cdot)\) 45.18.b.a 2 1
45.18.b.b 8
45.18.b.c 16
45.18.b.d 16
45.18.e \(\chi_{45}(16, \cdot)\) n/a 136 2
45.18.f \(\chi_{45}(8, \cdot)\) 45.18.f.a 68 2
45.18.j \(\chi_{45}(4, \cdot)\) n/a 200 2
45.18.l \(\chi_{45}(2, \cdot)\) n/a 400 4

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

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(45)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 1}\)