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Properties

Label 50.11
Level 50
Weight 11
Dimension 230
Nonzero newspaces 2
Newform subspaces 9
Sturm bound 1650
Trace bound 1

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Defining parameters

Level: \( N \) = \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 9 \)
Sturm bound: \(1650\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(50))\).

Total New Old
Modular forms 778 230 548
Cusp forms 722 230 492
Eisenstein series 56 0 56

Trace form

\( 230 q + 64 q^{2} + 248 q^{3} - 7560 q^{5} + 24320 q^{6} - 21208 q^{7} - 32768 q^{8} + O(q^{10}) \) \( 230 q + 64 q^{2} + 248 q^{3} - 7560 q^{5} + 24320 q^{6} - 21208 q^{7} - 32768 q^{8} + 94880 q^{10} - 903040 q^{11} + 126976 q^{12} + 1976868 q^{13} - 3637820 q^{15} + 5242880 q^{16} + 8635872 q^{17} - 1523104 q^{18} + 4829000 q^{19} - 194560 q^{20} - 32791240 q^{21} - 10671872 q^{22} + 7197088 q^{23} + 47345710 q^{25} + 11883520 q^{26} + 144581660 q^{27} - 36225024 q^{28} - 170869000 q^{29} - 111494400 q^{30} - 20948040 q^{31} + 25165824 q^{32} + 382498616 q^{33} - 291580000 q^{34} - 90354040 q^{35} - 272373760 q^{36} - 502346928 q^{37} - 293989120 q^{38} - 135682000 q^{39} - 6471680 q^{40} + 608001760 q^{41} + 145212928 q^{42} + 423764328 q^{43} + 66697110 q^{45} - 202983680 q^{46} - 3100116248 q^{47} - 65011712 q^{48} + 1147160800 q^{50} + 1559723560 q^{51} + 1012156416 q^{52} + 824139808 q^{53} - 3489062880 q^{55} - 538050560 q^{56} - 4048857120 q^{57} - 936757760 q^{58} - 3554994500 q^{59} + 4663357440 q^{60} + 3749700760 q^{61} - 4447232 q^{62} - 15408454252 q^{63} + 7311124010 q^{65} - 6050536960 q^{66} + 9399221032 q^{67} + 6187728896 q^{68} - 2334398500 q^{69} - 9349370240 q^{70} - 1541877440 q^{71} + 7282327552 q^{72} - 1796154372 q^{73} + 15342809460 q^{75} - 959180800 q^{76} + 40431757504 q^{77} - 3452722688 q^{78} + 8263862000 q^{79} + 1981808640 q^{80} + 20747670180 q^{81} - 8643348992 q^{82} - 29658467972 q^{83} - 16027392000 q^{84} - 6588253780 q^{85} + 472427520 q^{86} - 32940043860 q^{87} - 13830455296 q^{88} + 24935022250 q^{89} - 6785072480 q^{90} + 34742508360 q^{91} + 12502583296 q^{92} + 38704739956 q^{93} - 31881095960 q^{95} - 6375342080 q^{96} - 76804264028 q^{97} - 46670128576 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(50))\)

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
50.11.c \(\chi_{50}(7, \cdot)\) 50.11.c.a 2 2
50.11.c.b 2
50.11.c.c 2
50.11.c.d 2
50.11.c.e 6
50.11.c.f 8
50.11.c.g 8
50.11.f \(\chi_{50}(3, \cdot)\) 50.11.f.a 96 8
50.11.f.b 104

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(50)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 1}\)