Properties

Label 84.1
Level 84
Weight 1
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 384
Trace bound 0

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(384\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(84))\).

Total New Old
Modular forms 62 14 48
Cusp forms 2 2 0
Eisenstein series 60 12 48

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q - q^{3} - q^{7} - q^{9} + O(q^{10}) \) \( 2q - q^{3} - q^{7} - q^{9} - 2q^{13} + q^{19} + 2q^{21} - q^{25} + 2q^{27} + q^{31} + q^{37} + q^{39} - 2q^{43} - q^{49} - 2q^{57} - 2q^{61} - q^{63} + q^{67} + q^{73} - q^{75} + q^{79} - q^{81} + q^{91} + q^{93} + 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)

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
84.1.c \(\chi_{84}(29, \cdot)\) None 0 1
84.1.d \(\chi_{84}(13, \cdot)\) None 0 1
84.1.g \(\chi_{84}(43, \cdot)\) None 0 1
84.1.h \(\chi_{84}(83, \cdot)\) None 0 1
84.1.j \(\chi_{84}(47, \cdot)\) None 0 2
84.1.l \(\chi_{84}(67, \cdot)\) None 0 2
84.1.m \(\chi_{84}(61, \cdot)\) None 0 2
84.1.p \(\chi_{84}(53, \cdot)\) 84.1.p.a 2 2