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Properties

Label 2008.2
Level 2008
Weight 2
Dimension 70375
Nonzero newspaces 12
Sturm bound 504000
Trace bound 3

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Defining parameters

Level: \( N \) = \( 2008 = 2^{3} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(504000\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2008))\).

Total New Old
Modular forms 127500 71371 56129
Cusp forms 124501 70375 54126
Eisenstein series 2999 996 2003

Trace form

\( 70375 q - 250 q^{2} - 250 q^{3} - 250 q^{4} - 250 q^{6} - 250 q^{7} - 250 q^{8} - 500 q^{9} + O(q^{10}) \) \( 70375 q - 250 q^{2} - 250 q^{3} - 250 q^{4} - 250 q^{6} - 250 q^{7} - 250 q^{8} - 500 q^{9} - 250 q^{10} - 250 q^{11} - 250 q^{12} - 250 q^{14} - 250 q^{15} - 250 q^{16} - 500 q^{17} - 250 q^{18} - 250 q^{19} - 250 q^{20} - 250 q^{22} - 250 q^{23} - 250 q^{24} - 500 q^{25} - 250 q^{26} - 250 q^{27} - 250 q^{28} - 250 q^{30} - 250 q^{31} - 250 q^{32} - 500 q^{33} - 250 q^{34} - 250 q^{35} - 250 q^{36} - 250 q^{38} - 250 q^{39} - 250 q^{40} - 500 q^{41} - 250 q^{42} - 250 q^{43} - 250 q^{44} - 250 q^{46} - 250 q^{47} - 250 q^{48} - 500 q^{49} - 250 q^{50} - 250 q^{51} - 250 q^{52} - 250 q^{54} - 250 q^{55} - 250 q^{56} - 500 q^{57} - 250 q^{58} - 250 q^{59} - 250 q^{60} - 250 q^{62} - 250 q^{63} - 250 q^{64} - 500 q^{65} - 250 q^{66} - 250 q^{67} - 250 q^{68} - 250 q^{70} - 250 q^{71} - 250 q^{72} - 500 q^{73} - 250 q^{74} - 250 q^{75} - 250 q^{76} - 250 q^{78} - 250 q^{79} - 250 q^{80} - 500 q^{81} - 250 q^{82} - 250 q^{83} - 250 q^{84} - 250 q^{86} - 250 q^{87} - 250 q^{88} - 500 q^{89} - 250 q^{90} - 250 q^{91} - 250 q^{92} - 250 q^{94} - 250 q^{95} - 250 q^{96} - 500 q^{97} - 250 q^{98} - 250 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2008))\)

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
2008.2.a \(\chi_{2008}(1, \cdot)\) 2008.2.a.a 9 1
2008.2.a.b 12
2008.2.a.c 19
2008.2.a.d 23
2008.2.b \(\chi_{2008}(1005, \cdot)\) n/a 250 1
2008.2.e \(\chi_{2008}(2007, \cdot)\) None 0 1
2008.2.f \(\chi_{2008}(1003, \cdot)\) n/a 250 1
2008.2.i \(\chi_{2008}(113, \cdot)\) n/a 252 4
2008.2.k \(\chi_{2008}(283, \cdot)\) n/a 1000 4
2008.2.n \(\chi_{2008}(149, \cdot)\) n/a 1000 4
2008.2.o \(\chi_{2008}(231, \cdot)\) None 0 4
2008.2.q \(\chi_{2008}(25, \cdot)\) n/a 1260 20
2008.2.r \(\chi_{2008}(47, \cdot)\) None 0 20
2008.2.u \(\chi_{2008}(171, \cdot)\) n/a 5000 20
2008.2.v \(\chi_{2008}(5, \cdot)\) n/a 5000 20
2008.2.y \(\chi_{2008}(9, \cdot)\) n/a 6300 100
2008.2.ba \(\chi_{2008}(55, \cdot)\) None 0 100
2008.2.bc \(\chi_{2008}(11, \cdot)\) n/a 25000 100
2008.2.be \(\chi_{2008}(13, \cdot)\) n/a 25000 100

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2008))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2008)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(251))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(502))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1004))\)\(^{\oplus 2}\)