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Properties

Label 1004.2
Level 1004
Weight 2
Dimension 18125
Nonzero newspaces 8
Sturm bound 126000
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1004 = 2^{2} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(126000\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1004))\).

Total New Old
Modular forms 32125 18625 13500
Cusp forms 30876 18125 12751
Eisenstein series 1249 500 749

Trace form

\( 18125 q - 125 q^{2} - 125 q^{4} - 250 q^{5} - 125 q^{6} - 125 q^{8} - 250 q^{9} + O(q^{10}) \) \( 18125 q - 125 q^{2} - 125 q^{4} - 250 q^{5} - 125 q^{6} - 125 q^{8} - 250 q^{9} - 125 q^{10} - 125 q^{12} - 250 q^{13} - 125 q^{14} - 125 q^{16} - 250 q^{17} - 125 q^{18} - 125 q^{20} - 250 q^{21} - 125 q^{22} - 125 q^{24} - 250 q^{25} - 125 q^{26} - 125 q^{28} - 250 q^{29} - 125 q^{30} - 125 q^{32} - 250 q^{33} - 125 q^{34} - 125 q^{36} - 250 q^{37} - 125 q^{38} - 125 q^{40} - 250 q^{41} - 125 q^{42} - 125 q^{44} - 250 q^{45} - 125 q^{46} - 125 q^{48} - 250 q^{49} - 125 q^{50} - 125 q^{52} - 250 q^{53} - 125 q^{54} - 125 q^{56} - 250 q^{57} - 125 q^{58} - 125 q^{60} - 250 q^{61} - 125 q^{62} - 125 q^{64} - 250 q^{65} - 125 q^{66} - 125 q^{68} - 250 q^{69} - 125 q^{70} - 125 q^{72} - 250 q^{73} - 125 q^{74} - 125 q^{76} - 250 q^{77} - 125 q^{78} - 125 q^{80} - 250 q^{81} - 125 q^{82} - 125 q^{84} - 250 q^{85} - 125 q^{86} - 125 q^{88} - 250 q^{89} - 125 q^{90} - 125 q^{92} - 250 q^{93} - 125 q^{94} - 125 q^{96} - 250 q^{97} - 125 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1004))\)

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
1004.2.a \(\chi_{1004}(1, \cdot)\) 1004.2.a.a 7 1
1004.2.a.b 14
1004.2.c \(\chi_{1004}(1003, \cdot)\) n/a 124 1
1004.2.e \(\chi_{1004}(113, \cdot)\) 1004.2.e.a 84 4
1004.2.g \(\chi_{1004}(231, \cdot)\) n/a 496 4
1004.2.i \(\chi_{1004}(5, \cdot)\) n/a 420 20
1004.2.j \(\chi_{1004}(47, \cdot)\) n/a 2480 20
1004.2.m \(\chi_{1004}(9, \cdot)\) n/a 2100 100
1004.2.o \(\chi_{1004}(11, \cdot)\) n/a 12400 100

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1004))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(251))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(502))\)\(^{\oplus 2}\)