↑

Properties

Label 2008.1
Level 2008
Weight 1
Dimension 130
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 252000
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 2008 = 2^{3} \cdot 251 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(252000\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2008))\).

Total New Old
Modular forms 1656 628 1028
Cusp forms 156 130 26
Eisenstein series 1500 498 1002

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 130 0 0 0

Trace form

\( 130 q - q^{2} - 2 q^{3} + 5 q^{4} - 2 q^{6} - 2 q^{7} - q^{8} + 3 q^{9} + O(q^{10}) \) \( 130 q - q^{2} - 2 q^{3} + 5 q^{4} - 2 q^{6} - 2 q^{7} - q^{8} + 3 q^{9} - 2 q^{11} - 2 q^{12} + 5 q^{16} - 4 q^{17} - 3 q^{18} - 2 q^{19} - 4 q^{22} - 2 q^{23} - 2 q^{24} + 5 q^{25} - 4 q^{27} - 2 q^{28} - 2 q^{31} - q^{32} - 4 q^{33} - 2 q^{34} + 3 q^{36} - 4 q^{38} - 4 q^{41} - 2 q^{43} - 2 q^{44} - 2 q^{48} + 3 q^{49} - q^{50} - 4 q^{51} - 4 q^{54} - 4 q^{57} - 2 q^{58} - 2 q^{59} - 2 q^{63} + 5 q^{64} - 4 q^{66} - 2 q^{67} - 4 q^{68} - 3 q^{72} - 4 q^{73} - 2 q^{74} - 2 q^{75} - 2 q^{76} - 2 q^{79} + q^{81} - 2 q^{82} - 2 q^{83} - 4 q^{86} - 4 q^{88} - 4 q^{89} - 2 q^{92} - 2 q^{96} - 2 q^{97} - q^{98} - 6 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2008))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2008.1.c \(\chi_{2008}(501, \cdot)\) 2008.1.c.a 3 1
2008.1.c.b 3
2008.1.d \(\chi_{2008}(503, \cdot)\) None 0 1
2008.1.g \(\chi_{2008}(1507, \cdot)\) None 0 1
2008.1.h \(\chi_{2008}(1505, \cdot)\) None 0 1
2008.1.j \(\chi_{2008}(219, \cdot)\) 2008.1.j.a 4 4
2008.1.l \(\chi_{2008}(353, \cdot)\) None 0 4
2008.1.m \(\chi_{2008}(389, \cdot)\) None 0 4
2008.1.p \(\chi_{2008}(271, \cdot)\) None 0 4
2008.1.s \(\chi_{2008}(377, \cdot)\) None 0 20
2008.1.t \(\chi_{2008}(63, \cdot)\) None 0 20
2008.1.w \(\chi_{2008}(51, \cdot)\) 2008.1.w.a 20 20
2008.1.x \(\chi_{2008}(157, \cdot)\) None 0 20
2008.1.z \(\chi_{2008}(33, \cdot)\) None 0 100
2008.1.bb \(\chi_{2008}(7, \cdot)\) None 0 100
2008.1.bd \(\chi_{2008}(3, \cdot)\) 2008.1.bd.a 100 100
2008.1.bf \(\chi_{2008}(29, \cdot)\) None 0 100

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2008))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2008)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(251))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1004))\)\(^{\oplus 2}\)