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Properties

Label 201.5
Level 201
Weight 5
Dimension 4422
Nonzero newspaces 8
Sturm bound 14960
Trace bound 1

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Defining parameters

Level: \( N \) = \( 201 = 3 \cdot 67 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(14960\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(201))\).

Total New Old
Modular forms 6116 4550 1566
Cusp forms 5852 4422 1430
Eisenstein series 264 128 136

Trace form

\( 4422 q - 33 q^{3} - 66 q^{4} - 33 q^{6} - 66 q^{7} - 33 q^{9} + O(q^{10}) \) \( 4422 q - 33 q^{3} - 66 q^{4} - 33 q^{6} - 66 q^{7} - 33 q^{9} - 66 q^{10} - 33 q^{12} - 66 q^{13} - 33 q^{15} - 66 q^{16} - 33 q^{18} - 66 q^{19} - 33 q^{21} - 66 q^{22} - 33 q^{24} - 66 q^{25} - 33 q^{27} - 66 q^{28} - 33 q^{30} - 66 q^{31} - 33 q^{33} - 66 q^{34} - 33 q^{36} - 66 q^{37} - 33 q^{39} - 66 q^{40} - 33 q^{42} - 66 q^{43} - 33 q^{45} - 66 q^{46} - 33 q^{48} - 66 q^{49} - 33 q^{51} - 113410 q^{52} - 54054 q^{53} - 33 q^{54} - 24024 q^{55} + 47520 q^{56} + 22836 q^{57} + 109758 q^{58} + 63756 q^{59} + 133023 q^{60} + 127974 q^{61} + 57024 q^{62} + 3828 q^{63} + 163614 q^{64} + 34056 q^{65} - 66 q^{66} - 17622 q^{67} - 69696 q^{68} - 25575 q^{69} - 261954 q^{70} - 154440 q^{71} - 85569 q^{72} - 194260 q^{73} - 88704 q^{74} - 82005 q^{75} - 274626 q^{76} - 47916 q^{77} - 19041 q^{78} + 21956 q^{79} + 199584 q^{80} - 33 q^{81} + 291390 q^{82} + 138006 q^{83} + 123519 q^{84} - 66 q^{85} - 33 q^{87} - 66 q^{88} - 33 q^{90} - 66 q^{91} - 33 q^{93} - 66 q^{94} - 33 q^{96} - 66 q^{97} - 33 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(201))\)

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
201.5.b \(\chi_{201}(133, \cdot)\) 201.5.b.a 46 1
201.5.c \(\chi_{201}(68, \cdot)\) 201.5.c.a 88 1
201.5.g \(\chi_{201}(29, \cdot)\) n/a 178 2
201.5.h \(\chi_{201}(97, \cdot)\) 201.5.h.a 44 2
201.5.h.b 46
201.5.k \(\chi_{201}(14, \cdot)\) n/a 880 10
201.5.l \(\chi_{201}(43, \cdot)\) n/a 460 10
201.5.n \(\chi_{201}(7, \cdot)\) n/a 900 20
201.5.o \(\chi_{201}(17, \cdot)\) n/a 1780 20

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(201))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(201)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 2}\)