Properties

Label 2001.2.e
Level $2001$
Weight $2$
Character orbit 2001.e
Rep. character $\chi_{2001}(898,\cdot)$
Character field $\Q$
Dimension $112$
Sturm bound $480$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2001, [\chi])\).

Total New Old
Modular forms 244 112 132
Cusp forms 236 112 124
Eisenstein series 8 0 8

Trace form

\( 112q - 116q^{4} - 8q^{5} - 4q^{6} + 8q^{7} - 112q^{9} + O(q^{10}) \) \( 112q - 116q^{4} - 8q^{5} - 4q^{6} + 8q^{7} - 112q^{9} + 124q^{16} + 16q^{20} - 12q^{22} + 120q^{25} - 12q^{28} + 16q^{33} - 4q^{34} + 32q^{35} + 116q^{36} - 72q^{38} + 20q^{42} + 8q^{45} + 128q^{49} + 8q^{51} - 4q^{52} - 56q^{53} + 4q^{54} + 16q^{57} - 44q^{58} - 32q^{59} - 32q^{62} - 8q^{63} - 32q^{64} + 24q^{65} + 8q^{67} - 8q^{71} + 8q^{74} - 12q^{78} + 24q^{80} + 112q^{81} + 40q^{82} + 24q^{83} - 88q^{86} - 40q^{88} + 80q^{91} - 8q^{93} + 4q^{94} + 36q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2001, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2001, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2001, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(667, [\chi])\)\(^{\oplus 2}\)