Properties

Label 2100.2.bl
Level 2100
Weight 2
Character orbit bl
Rep. character \(\chi_{2100}(199,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 288
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.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
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 288 720
Cusp forms 912 288 624
Eisenstein series 96 0 96

Trace form

\( 288q + 144q^{9} + O(q^{10}) \) \( 288q + 144q^{9} - 20q^{14} + 16q^{16} + 28q^{44} - 8q^{46} + 24q^{49} + 68q^{56} + 96q^{64} + 72q^{66} + 56q^{74} - 144q^{81} + 8q^{84} + 4q^{86} + 72q^{94} + 60q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database