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Properties

Label 2001.2.bg
Level $2001$
Weight $2$
Character orbit 2001.bg
Rep. character $\chi_{2001}(41,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $4720$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.bg (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2001 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 4880 4880 0
Cusp forms 4720 4720 0
Eisenstein series 160 160 0

Trace form

\( 4720 q - 18 q^{3} - 72 q^{7} + O(q^{10}) \) \( 4720 q - 18 q^{3} - 72 q^{7} - 20 q^{10} - 16 q^{12} - 6 q^{15} + 312 q^{16} - 16 q^{18} - 28 q^{19} - 44 q^{21} - 400 q^{24} - 512 q^{25} + 36 q^{27} + 4 q^{30} - 52 q^{31} - 128 q^{36} - 52 q^{37} - 78 q^{39} - 12 q^{40} + 44 q^{43} - 40 q^{45} - 184 q^{46} + 32 q^{48} - 528 q^{49} - 136 q^{52} + 36 q^{54} - 64 q^{55} - 248 q^{58} - 58 q^{60} - 4 q^{61} + 212 q^{66} + 2 q^{69} - 48 q^{70} + 2 q^{72} - 72 q^{73} - 42 q^{75} - 52 q^{76} - 300 q^{78} + 68 q^{79} - 132 q^{81} - 40 q^{82} + 226 q^{84} - 24 q^{85} + 226 q^{87} + 216 q^{88} + 34 q^{90} - 32 q^{94} + 12 q^{97} - 150 q^{99} + O(q^{100}) \)

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.