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Properties

Label 2000.2.bd
Level $2000$
Weight $2$
Character orbit 2000.bd
Rep. character $\chi_{2000}(107,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1392$
Sturm bound $600$

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Defining parameters

Level: \( N \) \(=\) \( 2000 = 2^{4} \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2000.bd (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 400 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2000, [\chi])\).

Total New Old
Modular forms 2480 1488 992
Cusp forms 2320 1392 928
Eisenstein series 160 96 64

Trace form

\( 1392 q + 8 q^{2} + 6 q^{3} + 10 q^{4} - 18 q^{6} + 16 q^{7} + 2 q^{8} - 324 q^{9} + O(q^{10}) \) \( 1392 q + 8 q^{2} + 6 q^{3} + 10 q^{4} - 18 q^{6} + 16 q^{7} + 2 q^{8} - 324 q^{9} - 18 q^{11} + 10 q^{12} + 10 q^{13} + 10 q^{14} + 22 q^{16} + 16 q^{17} - 16 q^{18} + 10 q^{19} - 48 q^{21} - 28 q^{22} + 16 q^{23} + 36 q^{24} - 48 q^{26} - 6 q^{27} + 38 q^{28} + 10 q^{29} + 38 q^{32} + 16 q^{33} + 10 q^{34} + 30 q^{36} + 10 q^{37} + 34 q^{38} + 20 q^{39} - 6 q^{42} + 80 q^{44} - 18 q^{46} + 24 q^{47} - 100 q^{48} - 48 q^{51} + 16 q^{52} + 6 q^{53} - 20 q^{54} - 18 q^{56} - 12 q^{57} - 62 q^{58} + 10 q^{59} - 18 q^{61} - 26 q^{62} - 12 q^{63} - 20 q^{64} - 18 q^{66} + 70 q^{67} - 46 q^{68} + 46 q^{69} - 36 q^{71} + 96 q^{72} - 8 q^{73} - 24 q^{74} - 48 q^{76} + 48 q^{77} - 148 q^{78} - 288 q^{81} + 10 q^{82} + 46 q^{83} + 46 q^{84} - 138 q^{86} + 72 q^{87} - 6 q^{88} + 52 q^{91} + 6 q^{92} + 10 q^{94} - 48 q^{96} + 16 q^{97} - 88 q^{98} + 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2000, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2000, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2000, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)