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Properties

Label 2100.2.bg
Level $2100$
Weight $2$
Character orbit 2100.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

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

Display 100 coefficients 10 coefficients

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

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