Properties

Label 50.4
Level 50
Weight 4
Dimension 69
Nonzero newspaces 4
Newform subspaces 10
Sturm bound 600
Trace bound 1

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Defining parameters

Level: \( N \) = \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 10 \)
Sturm bound: \(600\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(50))\).

Total New Old
Modular forms 253 69 184
Cusp forms 197 69 128
Eisenstein series 56 0 56

Trace form

\( 69 q - 4 q^{2} + 16 q^{3} + 8 q^{4} + 5 q^{5} + 16 q^{6} + 8 q^{7} - 16 q^{8} - 166 q^{9} + O(q^{10}) \) \( 69 q - 4 q^{2} + 16 q^{3} + 8 q^{4} + 5 q^{5} + 16 q^{6} + 8 q^{7} - 16 q^{8} - 166 q^{9} - 50 q^{10} + 88 q^{11} + 64 q^{12} + 116 q^{13} + 224 q^{14} + 80 q^{15} - 96 q^{16} + 508 q^{17} + 302 q^{18} + 200 q^{19} - 80 q^{20} - 752 q^{21} - 768 q^{22} - 1144 q^{23} - 288 q^{24} - 1315 q^{25} - 304 q^{26} - 920 q^{27} - 208 q^{28} + 380 q^{29} + 360 q^{30} + 928 q^{31} + 96 q^{32} + 2112 q^{33} + 874 q^{34} + 1220 q^{35} + 72 q^{36} + 603 q^{37} + 400 q^{38} + 1608 q^{39} + 120 q^{40} + 368 q^{41} - 128 q^{42} - 344 q^{43} - 544 q^{44} - 2275 q^{45} - 64 q^{46} - 1312 q^{47} + 256 q^{48} - 219 q^{49} + 350 q^{50} - 1252 q^{51} + 464 q^{52} - 2109 q^{53} - 480 q^{54} - 1100 q^{55} - 768 q^{56} - 1040 q^{57} + 360 q^{58} + 4040 q^{59} + 2720 q^{60} + 2008 q^{61} + 4312 q^{62} + 11416 q^{63} + 128 q^{64} + 3085 q^{65} + 712 q^{66} + 608 q^{67} - 2448 q^{68} - 4512 q^{69} - 4800 q^{70} - 1312 q^{71} - 592 q^{72} - 6484 q^{73} - 5376 q^{74} - 12040 q^{75} - 1120 q^{76} - 10784 q^{77} - 8056 q^{78} - 6880 q^{79} + 80 q^{80} - 3526 q^{81} + 312 q^{82} + 3036 q^{83} + 1536 q^{84} + 6605 q^{85} + 456 q^{86} + 9040 q^{87} - 192 q^{88} + 10075 q^{89} + 8670 q^{90} + 5128 q^{91} + 3584 q^{92} + 5512 q^{93} + 2624 q^{94} - 2060 q^{95} + 256 q^{96} - 4072 q^{97} + 1308 q^{98} - 4252 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)

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
50.4.a \(\chi_{50}(1, \cdot)\) 50.4.a.a 1 1
50.4.a.b 1
50.4.a.c 1
50.4.a.d 1
50.4.a.e 1
50.4.b \(\chi_{50}(49, \cdot)\) 50.4.b.a 2 1
50.4.b.b 2
50.4.d \(\chi_{50}(11, \cdot)\) 50.4.d.a 12 4
50.4.d.b 16
50.4.e \(\chi_{50}(9, \cdot)\) 50.4.e.a 32 4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces

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