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

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

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

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