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Properties

Label 201.1
Level 201
Weight 1
Dimension 14
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 2992
Trace bound 1

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Defining parameters

Level: \( N \) = \( 201 = 3 \cdot 67 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(2992\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(201))\).

Total New Old
Modular forms 146 78 68
Cusp forms 14 14 0
Eisenstein series 132 64 68

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 10 4 0 0

Trace form

\( 14 q - q^{3} - q^{4} - 2 q^{6} - 4 q^{7} - 5 q^{9} + O(q^{10}) \) \( 14 q - q^{3} - q^{4} - 2 q^{6} - 4 q^{7} - 5 q^{9} - q^{12} - 4 q^{13} + q^{16} - 2 q^{21} - 4 q^{22} + 4 q^{24} + 3 q^{25} - q^{27} - 2 q^{28} - 2 q^{33} + 2 q^{34} - q^{36} - 4 q^{37} - 2 q^{39} + 4 q^{42} - 2 q^{43} - 2 q^{46} - q^{48} - 3 q^{49} - 2 q^{51} + 9 q^{52} + 2 q^{54} + 9 q^{57} - 4 q^{58} - 4 q^{61} + 11 q^{63} - 5 q^{64} - 5 q^{67} + 2 q^{69} + 11 q^{73} - q^{75} - 2 q^{76} - 2 q^{78} + 7 q^{79} + 3 q^{81} + 4 q^{82} + 9 q^{84} - 2 q^{87} + 2 q^{88} - 2 q^{93} - 4 q^{94} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(201))\)

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
201.1.b \(\chi_{201}(133, \cdot)\) None 0 1
201.1.c \(\chi_{201}(68, \cdot)\) None 0 1
201.1.g \(\chi_{201}(29, \cdot)\) 201.1.g.a 4 2
201.1.h \(\chi_{201}(97, \cdot)\) None 0 2
201.1.k \(\chi_{201}(14, \cdot)\) 201.1.k.a 10 10
201.1.l \(\chi_{201}(43, \cdot)\) None 0 10
201.1.n \(\chi_{201}(7, \cdot)\) None 0 20
201.1.o \(\chi_{201}(17, \cdot)\) None 0 20