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 $480$

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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

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

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

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