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Properties

Label 2000.2.bl
Level $2000$
Weight $2$
Character orbit 2000.bl
Rep. character $\chi_{2000}(149,\cdot)$
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.bl (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

\( 1392 q + 10 q^{2} + 10 q^{3} + 6 q^{4} - 18 q^{6} + 40 q^{8} + O(q^{10}) \) \( 1392 q + 10 q^{2} + 10 q^{3} + 6 q^{4} - 18 q^{6} + 40 q^{8} - 18 q^{11} + 10 q^{12} + 10 q^{13} - 30 q^{14} - 18 q^{16} + 20 q^{17} + 6 q^{19} + 10 q^{22} + 16 q^{24} - 28 q^{26} + 10 q^{27} + 50 q^{28} + 6 q^{29} - 12 q^{31} + 20 q^{33} + 14 q^{34} - 126 q^{36} + 10 q^{37} - 60 q^{38} + 70 q^{42} - 36 q^{44} - 26 q^{46} + 20 q^{47} + 140 q^{48} + 1136 q^{49} - 36 q^{51} - 80 q^{52} + 10 q^{53} + 30 q^{54} + 24 q^{56} + 10 q^{58} + 6 q^{59} - 18 q^{61} + 10 q^{62} + 160 q^{63} + 24 q^{64} + 80 q^{66} + 70 q^{67} + 42 q^{69} + 10 q^{72} - 28 q^{74} - 108 q^{76} + 80 q^{77} + 10 q^{78} + 52 q^{79} + 216 q^{81} + 10 q^{83} - 196 q^{84} - 58 q^{86} - 100 q^{88} + 24 q^{91} - 80 q^{92} - 106 q^{94} - 78 q^{96} + 20 q^{97} + 100 q^{98} + 16 q^{99} + O(q^{100}) \)

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

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