Properties

Label 944.1
Level 944
Weight 1
Dimension 8
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 55680
Trace bound 3

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 944 = 2^{4} \cdot 59 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(55680\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(944))\).

Total New Old
Modular forms 894 265 629
Cusp forms 82 8 74
Eisenstein series 812 257 555

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

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

Trace form

\( 8 q + q^{3} - 5 q^{5} + q^{7} + 3 q^{9} + O(q^{10}) \) \( 8 q + q^{3} - 5 q^{5} + q^{7} + 3 q^{9} + 2 q^{15} - 4 q^{16} + 3 q^{17} + 5 q^{19} + 4 q^{20} - 2 q^{21} - 4 q^{22} + 3 q^{25} + 2 q^{27} - 4 q^{28} - q^{29} + 6 q^{35} - 4 q^{36} - q^{41} + q^{45} - 4 q^{46} + 3 q^{49} + 2 q^{51} - q^{53} - 2 q^{57} - 4 q^{59} - 4 q^{62} - 10 q^{63} + q^{71} + 4 q^{74} - 6 q^{75} + 4 q^{76} + 5 q^{79} + 4 q^{80} - 2 q^{81} - 6 q^{85} + 4 q^{86} + 2 q^{87} - 15 q^{95} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(944))\)

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
944.1.c \(\chi_{944}(825, \cdot)\) None 0 1
944.1.d \(\chi_{944}(591, \cdot)\) None 0 1
944.1.g \(\chi_{944}(119, \cdot)\) None 0 1
944.1.h \(\chi_{944}(353, \cdot)\) 944.1.h.a 1 1
944.1.h.b 3
944.1.j \(\chi_{944}(117, \cdot)\) 944.1.j.a 4 2
944.1.l \(\chi_{944}(355, \cdot)\) None 0 2
944.1.n \(\chi_{944}(33, \cdot)\) None 0 28
944.1.o \(\chi_{944}(7, \cdot)\) None 0 28
944.1.r \(\chi_{944}(15, \cdot)\) None 0 28
944.1.s \(\chi_{944}(73, \cdot)\) None 0 28
944.1.u \(\chi_{944}(3, \cdot)\) None 0 56
944.1.w \(\chi_{944}(13, \cdot)\) None 0 56

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(944))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(944)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(236))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(472))\)\(^{\oplus 2}\)