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Properties

Label 50.10
Level 50
Weight 10
Dimension 208
Nonzero newspaces 4
Newform subspaces 19
Sturm bound 1500
Trace bound 3

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Defining parameters

Level: \( N \) = \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 19 \)
Sturm bound: \(1500\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(50))\).

Total New Old
Modular forms 703 208 495
Cusp forms 647 208 439
Eisenstein series 56 0 56

Trace form

\( 208 q - 16 q^{2} + 436 q^{3} - 256 q^{4} + 2335 q^{5} + 6592 q^{6} + 3312 q^{7} - 4096 q^{8} + 100067 q^{9} + O(q^{10}) \) \( 208 q - 16 q^{2} + 436 q^{3} - 256 q^{4} + 2335 q^{5} + 6592 q^{6} + 3312 q^{7} - 4096 q^{8} + 100067 q^{9} - 58960 q^{10} + 180996 q^{11} + 111616 q^{12} - 68334 q^{13} - 629888 q^{14} - 243520 q^{15} - 1114112 q^{16} - 406978 q^{17} + 2201792 q^{18} + 172380 q^{19} - 1182720 q^{20} + 2162416 q^{21} + 550848 q^{22} + 632416 q^{23} + 3342336 q^{24} + 16993135 q^{25} + 4379232 q^{26} - 28656560 q^{27} - 11639808 q^{28} - 20983070 q^{29} + 25154880 q^{30} + 20745856 q^{31} + 4194304 q^{32} - 24300528 q^{33} - 38182288 q^{34} - 33082460 q^{35} - 48082176 q^{36} - 13183633 q^{37} + 47700160 q^{38} + 127927584 q^{39} + 13086720 q^{40} + 26014106 q^{41} - 83712512 q^{42} - 86894924 q^{43} - 59784192 q^{44} - 305202445 q^{45} - 23097728 q^{46} + 136287472 q^{47} + 28573696 q^{48} + 520495428 q^{49} + 78642800 q^{50} + 252243716 q^{51} - 17493504 q^{52} - 709813209 q^{53} - 735657600 q^{54} - 517242940 q^{55} + 28278784 q^{56} + 932434720 q^{57} + 545717280 q^{58} + 763835940 q^{59} - 183531520 q^{60} + 38956966 q^{61} - 144813632 q^{62} - 170494304 q^{63} - 16777216 q^{64} + 1333812935 q^{65} - 317493056 q^{66} - 719617788 q^{67} - 678486528 q^{68} - 501676416 q^{69} - 431771520 q^{70} - 580173784 q^{71} - 108187648 q^{72} + 634493766 q^{73} + 854255072 q^{74} + 3623806760 q^{75} - 95953920 q^{76} - 1207356896 q^{77} + 1292283584 q^{78} + 239493360 q^{79} + 153026560 q^{80} - 3432353497 q^{81} - 3798471072 q^{82} - 2163209504 q^{83} - 428777472 q^{84} + 4161327175 q^{85} + 50444032 q^{86} + 9216748360 q^{87} + 1012482048 q^{88} - 1526411085 q^{89} - 4403622480 q^{90} - 3044007144 q^{91} - 1686759424 q^{92} + 55087192 q^{93} - 3620711168 q^{94} - 1752576060 q^{95} + 432013312 q^{96} + 5027625282 q^{97} + 4258820208 q^{98} + 9316081904 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(50))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
50.10.a \(\chi_{50}(1, \cdot)\) 50.10.a.a 1 1
50.10.a.b 1
50.10.a.c 1
50.10.a.d 1
50.10.a.e 1
50.10.a.f 1
50.10.a.g 2
50.10.a.h 2
50.10.a.i 2
50.10.a.j 2
50.10.b \(\chi_{50}(49, \cdot)\) 50.10.b.a 2 1
50.10.b.b 2
50.10.b.c 2
50.10.b.d 2
50.10.b.e 2
50.10.b.f 4
50.10.d \(\chi_{50}(11, \cdot)\) 50.10.d.a 44 4
50.10.d.b 48
50.10.e \(\chi_{50}(9, \cdot)\) 50.10.e.a 88 4

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces

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