Properties

Label 2100.2.bg
Level 2100
Weight 2
Character orbit bg
Rep. character \(\chi_{2100}(851,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 584
Sturm bound 960

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Defining parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.bg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2100, [\chi])\).

Total New Old
Modular forms 1008 632 376
Cusp forms 912 584 328
Eisenstein series 96 48 48

Trace form

\( 584q + 2q^{4} - 16q^{6} + 2q^{9} + O(q^{10}) \) \( 584q + 2q^{4} - 16q^{6} + 2q^{9} + 2q^{12} + 8q^{13} - 14q^{16} - 10q^{21} + 28q^{22} - 18q^{24} + 2q^{28} - 10q^{33} + 24q^{34} + 12q^{36} + 16q^{42} - 16q^{46} + 28q^{48} + 24q^{49} - 4q^{52} + 8q^{54} + 4q^{57} + 2q^{58} - 4q^{61} + 44q^{64} - 38q^{66} + 44q^{69} - 14q^{72} + 24q^{73} - 72q^{76} + 8q^{78} - 34q^{81} + 44q^{82} - 18q^{84} + 26q^{88} + 22q^{93} + 20q^{94} + 24q^{96} + 24q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2100, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database