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Properties

Label 201.4
Level 201
Weight 4
Dimension 3300
Nonzero newspaces 8
Newform subspaces 17
Sturm bound 11968
Trace bound 1

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Defining parameters

Level: \( N \) = \( 201 = 3 \cdot 67 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 17 \)
Sturm bound: \(11968\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(201))\).

Total New Old
Modular forms 4620 3432 1188
Cusp forms 4356 3300 1056
Eisenstein series 264 132 132

Trace form

\( 3300 q - 33 q^{3} - 66 q^{4} - 33 q^{6} - 66 q^{7} - 33 q^{9} + O(q^{10}) \) \( 3300 q - 33 q^{3} - 66 q^{4} - 33 q^{6} - 66 q^{7} - 33 q^{9} - 66 q^{10} - 33 q^{12} - 66 q^{13} - 33 q^{15} - 66 q^{16} - 33 q^{18} - 66 q^{19} - 33 q^{21} - 66 q^{22} - 33 q^{24} - 66 q^{25} - 33 q^{27} - 66 q^{28} - 33 q^{30} - 66 q^{31} - 33 q^{33} - 66 q^{34} - 33 q^{36} - 66 q^{37} - 33 q^{39} - 66 q^{40} - 33 q^{42} - 66 q^{43} - 33 q^{45} - 66 q^{46} - 33 q^{48} - 66 q^{49} - 33 q^{51} + 12606 q^{52} + 7656 q^{53} - 33 q^{54} + 13002 q^{55} + 17424 q^{56} + 1815 q^{57} + 1518 q^{58} - 1320 q^{59} - 6369 q^{60} - 9570 q^{61} - 6072 q^{62} - 627 q^{63} - 39666 q^{64} - 16896 q^{65} - 17424 q^{66} - 8778 q^{67} - 16896 q^{68} - 3993 q^{69} - 28578 q^{70} - 12144 q^{71} - 4785 q^{72} - 6930 q^{73} - 1320 q^{74} + 759 q^{75} + 12606 q^{76} + 5808 q^{77} + 8679 q^{78} + 13794 q^{79} + 45936 q^{80} - 33 q^{81} + 34386 q^{82} + 13596 q^{83} + 10527 q^{84} - 66 q^{85} - 33 q^{87} - 66 q^{88} - 33 q^{90} - 66 q^{91} - 33 q^{93} - 66 q^{94} - 33 q^{96} - 66 q^{97} - 33 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(201))\)

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
201.4.a \(\chi_{201}(1, \cdot)\) 201.4.a.a 1 1
201.4.a.b 6
201.4.a.c 7
201.4.a.d 9
201.4.a.e 11
201.4.d \(\chi_{201}(200, \cdot)\) 201.4.d.a 2 1
201.4.d.b 64
201.4.e \(\chi_{201}(37, \cdot)\) 201.4.e.a 32 2
201.4.e.b 36
201.4.f \(\chi_{201}(38, \cdot)\) 201.4.f.a 132 2
201.4.i \(\chi_{201}(22, \cdot)\) 201.4.i.a 170 10
201.4.i.b 170
201.4.j \(\chi_{201}(5, \cdot)\) 201.4.j.a 20 10
201.4.j.b 640
201.4.m \(\chi_{201}(4, \cdot)\) 201.4.m.a 320 20
201.4.m.b 360
201.4.p \(\chi_{201}(2, \cdot)\) 201.4.p.a 1320 20

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(201))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(201)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 2}\)