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Properties

Label 2001.2.y
Level $2001$
Weight $2$
Character orbit 2001.y
Rep. character $\chi_{2001}(202,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1200$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.y (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 2440 1200 1240
Cusp forms 2360 1200 1160
Eisenstein series 80 0 80

Trace form

\( 1200 q + 112 q^{4} + 8 q^{7} + 120 q^{9} + O(q^{10}) \) \( 1200 q + 112 q^{4} + 8 q^{7} + 120 q^{9} + 8 q^{13} - 200 q^{16} + 80 q^{22} - 84 q^{23} - 40 q^{25} + 22 q^{29} - 24 q^{30} - 16 q^{33} + 16 q^{34} + 24 q^{35} - 156 q^{36} + 228 q^{38} + 8 q^{42} - 144 q^{49} + 56 q^{51} + 8 q^{52} - 16 q^{53} - 8 q^{57} + 10 q^{58} + 32 q^{59} + 72 q^{62} - 8 q^{63} + 48 q^{64} - 16 q^{65} + 52 q^{67} - 48 q^{71} + 28 q^{74} + 16 q^{78} - 348 q^{80} - 120 q^{81} - 88 q^{82} - 152 q^{83} - 108 q^{86} + 24 q^{87} + 352 q^{88} + 256 q^{91} + 12 q^{92} - 32 q^{93} + 48 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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