Properties

Label 1002.2
Level 1002
Weight 2
Dimension 6973
Nonzero newspaces 4
Sturm bound 111552
Trace bound 1

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1002 = 2 \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(111552\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1002))\).

Total New Old
Modular forms 28552 6973 21579
Cusp forms 27225 6973 20252
Eisenstein series 1327 0 1327

Trace form

\(6973q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6973q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 12q^{11} \) \(\mathstrut +\mathstrut q^{12} \) \(\mathstrut +\mathstrut 14q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut +\mathstrut 6q^{20} \) \(\mathstrut +\mathstrut 8q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut 31q^{25} \) \(\mathstrut +\mathstrut 14q^{26} \) \(\mathstrut +\mathstrut q^{27} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 30q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut +\mathstrut 32q^{31} \) \(\mathstrut +\mathstrut q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut +\mathstrut 18q^{34} \) \(\mathstrut +\mathstrut 48q^{35} \) \(\mathstrut +\mathstrut q^{36} \) \(\mathstrut +\mathstrut 38q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut +\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 44q^{43} \) \(\mathstrut +\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 48q^{47} \) \(\mathstrut +\mathstrut q^{48} \) \(\mathstrut +\mathstrut 57q^{49} \) \(\mathstrut +\mathstrut 31q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 14q^{52} \) \(\mathstrut +\mathstrut 54q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut +\mathstrut 72q^{55} \) \(\mathstrut +\mathstrut 8q^{56} \) \(\mathstrut +\mathstrut 20q^{57} \) \(\mathstrut +\mathstrut 30q^{58} \) \(\mathstrut +\mathstrut 60q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 62q^{61} \) \(\mathstrut +\mathstrut 32q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut q^{64} \) \(\mathstrut +\mathstrut 84q^{65} \) \(\mathstrut +\mathstrut 12q^{66} \) \(\mathstrut +\mathstrut 68q^{67} \) \(\mathstrut +\mathstrut 18q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 48q^{70} \) \(\mathstrut +\mathstrut 72q^{71} \) \(\mathstrut +\mathstrut q^{72} \) \(\mathstrut +\mathstrut 74q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut +\mathstrut 31q^{75} \) \(\mathstrut +\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 80q^{79} \) \(\mathstrut +\mathstrut 6q^{80} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut +\mathstrut 42q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 108q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 30q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 90q^{89} \) \(\mathstrut +\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 112q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 48q^{94} \) \(\mathstrut +\mathstrut 120q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 57q^{98} \) \(\mathstrut +\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1002))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1002.2.a \(\chi_{1002}(1, \cdot)\) 1002.2.a.a 1 1
1002.2.a.b 1
1002.2.a.c 1
1002.2.a.d 1
1002.2.a.e 1
1002.2.a.f 2
1002.2.a.g 3
1002.2.a.h 3
1002.2.a.i 4
1002.2.a.j 5
1002.2.a.k 7
1002.2.d \(\chi_{1002}(1001, \cdot)\) 1002.2.d.a 56 1
1002.2.e \(\chi_{1002}(7, \cdot)\) n/a 2296 82
1002.2.f \(\chi_{1002}(5, \cdot)\) n/a 4592 82

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1002))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(501))\)\(^{\oplus 2}\)