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Properties

Label 2001.2.k
Level $2001$
Weight $2$
Character orbit 2001.k
Rep. character $\chi_{2001}(505,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $240$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 488 240 248
Cusp forms 472 240 232
Eisenstein series 16 0 16

Trace form

\( 240 q + 8 q^{2} - 8 q^{8} + O(q^{10}) \) \( 240 q + 8 q^{2} - 8 q^{8} - 224 q^{16} - 8 q^{18} + 24 q^{23} + 208 q^{25} - 24 q^{26} + 8 q^{31} + 32 q^{32} - 240 q^{36} - 16 q^{39} + 8 q^{41} - 20 q^{46} - 24 q^{47} - 224 q^{49} + 16 q^{50} - 56 q^{55} + 24 q^{58} + 16 q^{59} - 72 q^{70} - 8 q^{72} + 40 q^{73} - 16 q^{75} + 56 q^{77} - 240 q^{81} - 48 q^{82} - 40 q^{85} - 8 q^{87} + 32 q^{94} + 16 q^{95} - 136 q^{98} + O(q^{100}) \)

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

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