Properties

Label 164.1
Level 164
Weight 1
Dimension 11
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 1680
Trace bound 5

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Defining parameters

Level: \( N \) = \( 164 = 2^{2} \cdot 41 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(1680\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(164))\).

Total New Old
Modular forms 111 49 62
Cusp forms 11 11 0
Eisenstein series 100 38 62

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 11 0 0 0

Trace form

\( 11q - 3q^{2} + q^{4} - 2q^{5} - 3q^{8} + q^{9} + O(q^{10}) \) \( 11q - 3q^{2} + q^{4} - 2q^{5} - 3q^{8} + q^{9} - 2q^{10} - 2q^{13} + q^{16} - 2q^{17} - 3q^{18} - 2q^{20} - 4q^{21} - 5q^{25} - 2q^{26} - 2q^{29} + 7q^{32} - 4q^{33} + 8q^{34} + q^{36} - 2q^{37} - 2q^{40} + q^{41} + 4q^{42} - 2q^{45} + q^{49} + 9q^{50} + 8q^{52} - 2q^{53} + 4q^{57} - 2q^{58} - 6q^{61} + q^{64} + 6q^{65} + 4q^{66} - 2q^{68} - 3q^{72} - 2q^{73} - 2q^{74} + 4q^{77} - 2q^{80} + 7q^{81} - 3q^{82} - 4q^{84} + 6q^{85} - 2q^{89} - 2q^{90} - 2q^{97} - 3q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(164))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
164.1.c \(\chi_{164}(83, \cdot)\) None 0 1
164.1.d \(\chi_{164}(163, \cdot)\) 164.1.d.a 1 1
164.1.d.b 2
164.1.e \(\chi_{164}(91, \cdot)\) None 0 2
164.1.h \(\chi_{164}(85, \cdot)\) None 0 4
164.1.j \(\chi_{164}(51, \cdot)\) 164.1.j.a 4 4
164.1.l \(\chi_{164}(23, \cdot)\) 164.1.l.a 4 4
164.1.n \(\chi_{164}(39, \cdot)\) None 0 8
164.1.p \(\chi_{164}(13, \cdot)\) None 0 16