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Properties

Label 2001.2.r
Level $2001$
Weight $2$
Character orbit 2001.r
Rep. character $\chi_{2001}(208,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $672$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.r (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1464 672 792
Cusp forms 1416 672 744
Eisenstein series 48 0 48

Trace form

\( 672 q + 116 q^{4} + 8 q^{5} + 4 q^{6} - 8 q^{7} + 112 q^{9} + O(q^{10}) \) \( 672 q + 116 q^{4} + 8 q^{5} + 4 q^{6} - 8 q^{7} + 112 q^{9} + 28 q^{15} - 124 q^{16} + 40 q^{20} - 44 q^{22} - 36 q^{25} - 56 q^{26} + 96 q^{28} - 28 q^{29} - 28 q^{31} - 16 q^{33} - 52 q^{34} - 32 q^{35} - 116 q^{36} + 84 q^{37} + 16 q^{38} - 20 q^{42} + 20 q^{45} + 56 q^{47} - 128 q^{49} - 196 q^{50} + 20 q^{51} + 4 q^{52} - 28 q^{53} - 4 q^{54} - 28 q^{55} - 196 q^{56} - 16 q^{57} - 124 q^{58} - 24 q^{59} - 84 q^{60} + 56 q^{61} - 164 q^{62} - 20 q^{63} + 32 q^{64} - 52 q^{65} + 168 q^{66} + 48 q^{67} - 28 q^{68} + 8 q^{71} + 168 q^{73} - 8 q^{74} + 140 q^{76} + 140 q^{77} + 12 q^{78} - 24 q^{80} - 112 q^{81} - 96 q^{82} + 88 q^{83} + 88 q^{86} - 128 q^{88} - 80 q^{91} + 8 q^{93} + 136 q^{94} + 104 q^{96} - 84 q^{97} + 224 q^{98} + O(q^{100}) \)

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

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