↑

Properties

Label 1024.4
Level 1024
Weight 4
Dimension 55056
Nonzero newspaces 8
Sturm bound 262144
Trace bound 9

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 1024 = 2^{10} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(262144\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1024))\).

Total New Old
Modular forms 99136 55536 43600
Cusp forms 97472 55056 42416
Eisenstein series 1664 480 1184

Trace form

\( 55056 q - 128 q^{2} - 96 q^{3} - 128 q^{4} - 128 q^{5} - 128 q^{6} - 96 q^{7} - 128 q^{8} - 160 q^{9} + O(q^{10}) \) \( 55056 q - 128 q^{2} - 96 q^{3} - 128 q^{4} - 128 q^{5} - 128 q^{6} - 96 q^{7} - 128 q^{8} - 160 q^{9} - 128 q^{10} - 96 q^{11} - 128 q^{12} - 128 q^{13} - 128 q^{14} - 96 q^{15} - 128 q^{16} - 192 q^{17} - 128 q^{18} - 96 q^{19} - 128 q^{20} - 128 q^{21} - 128 q^{22} - 96 q^{23} - 128 q^{24} - 160 q^{25} - 128 q^{26} - 96 q^{27} - 128 q^{28} - 128 q^{29} - 128 q^{30} - 96 q^{31} - 128 q^{32} - 224 q^{33} - 128 q^{34} - 96 q^{35} - 128 q^{36} - 128 q^{37} - 128 q^{38} - 96 q^{39} - 128 q^{40} - 160 q^{41} - 128 q^{42} - 96 q^{43} - 128 q^{44} - 128 q^{45} - 128 q^{46} - 96 q^{47} - 128 q^{48} - 192 q^{49} - 128 q^{50} - 96 q^{51} - 128 q^{52} - 128 q^{53} - 128 q^{54} - 96 q^{55} - 128 q^{56} - 160 q^{57} - 128 q^{58} - 96 q^{59} - 128 q^{60} - 128 q^{61} - 128 q^{62} - 96 q^{63} - 128 q^{64} - 256 q^{65} - 128 q^{66} - 96 q^{67} - 128 q^{68} - 128 q^{69} - 128 q^{70} - 96 q^{71} - 128 q^{72} - 160 q^{73} - 128 q^{74} - 96 q^{75} - 128 q^{76} - 128 q^{77} - 128 q^{78} - 96 q^{79} - 128 q^{80} - 192 q^{81} - 128 q^{82} - 96 q^{83} - 128 q^{84} - 128 q^{85} - 128 q^{86} - 96 q^{87} - 128 q^{88} - 160 q^{89} - 128 q^{90} - 96 q^{91} - 128 q^{92} - 128 q^{93} - 128 q^{94} - 96 q^{95} - 128 q^{96} - 224 q^{97} - 128 q^{98} - 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1024))\)

We only show spaces with even 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
1024.4.a \(\chi_{1024}(1, \cdot)\) 1024.4.a.a 2 1
1024.4.a.b 2
1024.4.a.c 2
1024.4.a.d 2
1024.4.a.e 4
1024.4.a.f 4
1024.4.a.g 4
1024.4.a.h 4
1024.4.a.i 4
1024.4.a.j 4
1024.4.a.k 8
1024.4.a.l 8
1024.4.a.m 10
1024.4.a.n 10
1024.4.a.o 12
1024.4.a.p 12
1024.4.b \(\chi_{1024}(513, \cdot)\) 1024.4.b.a 2 1
1024.4.b.b 2
1024.4.b.c 2
1024.4.b.d 2
1024.4.b.e 4
1024.4.b.f 4
1024.4.b.g 4
1024.4.b.h 4
1024.4.b.i 8
1024.4.b.j 10
1024.4.b.k 10
1024.4.b.l 16
1024.4.b.m 24
1024.4.e \(\chi_{1024}(257, \cdot)\) n/a 184 2
1024.4.g \(\chi_{1024}(129, \cdot)\) n/a 384 4
1024.4.i \(\chi_{1024}(65, \cdot)\) n/a 736 8
1024.4.k \(\chi_{1024}(33, \cdot)\) n/a 1504 16
1024.4.m \(\chi_{1024}(17, \cdot)\) n/a 3040 32
1024.4.o \(\chi_{1024}(9, \cdot)\) None 0 64
1024.4.q \(\chi_{1024}(5, \cdot)\) n/a 49024 128

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1024))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1024)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(512))\)\(^{\oplus 2}\)