Properties

Label 50.9
Level 50
Weight 9
Dimension 184
Nonzero newspaces 2
Newform subspaces 8
Sturm bound 1350
Trace bound 1

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Defining parameters

Level: \( N \) = \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 8 \)
Sturm bound: \(1350\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(50))\).

Total New Old
Modular forms 628 184 444
Cusp forms 572 184 388
Eisenstein series 56 0 56

Trace form

\( 184 q - 280 q^{3} + 780 q^{5} - 1024 q^{6} - 9080 q^{7} + O(q^{10}) \) \( 184 q - 280 q^{3} + 780 q^{5} - 1024 q^{6} - 9080 q^{7} + 6400 q^{10} + 69168 q^{11} - 35840 q^{12} - 238560 q^{13} + 252580 q^{15} + 262144 q^{16} + 336180 q^{17} - 317440 q^{18} - 1437800 q^{19} - 161280 q^{20} + 598328 q^{21} + 1940480 q^{22} + 1391520 q^{23} - 3015940 q^{25} - 927744 q^{26} - 3183580 q^{27} + 1059840 q^{28} + 3913800 q^{29} + 5352960 q^{30} + 1696008 q^{31} - 4164520 q^{33} - 10304000 q^{34} - 2665680 q^{35} + 1236992 q^{36} + 3982080 q^{37} + 10152960 q^{38} + 22510400 q^{39} - 1146880 q^{40} - 21657552 q^{41} - 26301440 q^{42} - 38495640 q^{43} + 48565500 q^{45} + 34820096 q^{46} + 44007720 q^{47} + 4587520 q^{48} - 5414400 q^{50} - 61195472 q^{51} - 30535680 q^{52} - 100767360 q^{53} + 41350200 q^{55} + 28311552 q^{56} + 171395520 q^{57} + 48389120 q^{58} - 96239100 q^{59} + 11627520 q^{60} + 7546088 q^{61} - 7088640 q^{62} - 206014900 q^{63} - 173478540 q^{65} + 55903232 q^{66} + 11911160 q^{67} + 78927360 q^{68} + 256837700 q^{69} + 115673600 q^{70} - 24006432 q^{71} - 40632320 q^{72} + 265225440 q^{73} - 262176540 q^{75} - 33336320 q^{76} - 237209520 q^{77} - 214607360 q^{78} - 277012400 q^{79} - 12779520 q^{80} - 240206736 q^{81} - 19701760 q^{82} + 594720900 q^{83} + 387110400 q^{84} + 648719080 q^{85} + 353865216 q^{86} - 240100860 q^{87} + 10485760 q^{88} - 999182700 q^{89} - 739278080 q^{90} + 111682008 q^{91} + 89986560 q^{92} + 842135020 q^{93} + 582691440 q^{95} + 16777216 q^{96} - 216146800 q^{97} - 230338560 q^{98} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(50))\)

We only show spaces with odd 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
50.9.c \(\chi_{50}(7, \cdot)\) 50.9.c.a 4 2
50.9.c.b 4
50.9.c.c 4
50.9.c.d 4
50.9.c.e 4
50.9.c.f 4
50.9.f \(\chi_{50}(3, \cdot)\) 50.9.f.a 80 8
50.9.f.b 80

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(50)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 1}\)