Properties

Label 1028.1
Level 1028
Weight 1
Dimension 71
Nonzero newspaces 6
Newform subspaces 9
Sturm bound 66048
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1028 = 2^{2} \cdot 257 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 9 \)
Sturm bound: \(66048\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1028))\).

Total New Old
Modular forms 711 325 386
Cusp forms 71 71 0
Eisenstein series 640 254 386

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 71 0 0 0

Trace form

\( 71 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - q^{8} + 3 q^{9} + O(q^{10}) \) \( 71 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - q^{8} + 3 q^{9} - 2 q^{10} - 8 q^{13} + 4 q^{16} - 2 q^{18} - 2 q^{20} - 4 q^{21} - 3 q^{22} + 5 q^{25} - 5 q^{26} - 4 q^{32} - 3 q^{34} + 6 q^{36} - 2 q^{37} - 2 q^{40} - 2 q^{41} - 4 q^{42} + 3 q^{44} - 2 q^{45} - 3 q^{46} + 3 q^{49} - 6 q^{50} - 5 q^{52} - 2 q^{53} - 4 q^{57} - 3 q^{58} - 6 q^{61} - 3 q^{62} + 7 q^{64} - 4 q^{65} - 3 q^{68} - 5 q^{72} - 2 q^{74} - 2 q^{80} + 3 q^{81} - 2 q^{82} - 4 q^{84} - 4 q^{85} - 8 q^{89} - 2 q^{90} + 3 q^{92} - 2 q^{97} - 2 q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1028))\)

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
1028.1.c \(\chi_{1028}(515, \cdot)\) None 0 1
1028.1.d \(\chi_{1028}(1027, \cdot)\) 1028.1.d.a 1 1
1028.1.d.b 2
1028.1.d.c 2
1028.1.d.d 4
1028.1.e \(\chi_{1028}(755, \cdot)\) 1028.1.e.a 2 2
1028.1.h \(\chi_{1028}(707, \cdot)\) 1028.1.h.a 4 4
1028.1.j \(\chi_{1028}(255, \cdot)\) 1028.1.j.a 8 8
1028.1.l \(\chi_{1028}(15, \cdot)\) 1028.1.l.a 16 16
1028.1.m \(\chi_{1028}(11, \cdot)\) 1028.1.m.a 32 32
1028.1.o \(\chi_{1028}(31, \cdot)\) None 0 64
1028.1.r \(\chi_{1028}(5, \cdot)\) None 0 128