Properties

Label 2100.2.l
Level 2100
Weight 2
Character orbit l
Rep. character \(\chi_{2100}(1499,\cdot)\)
Character field \(\Q\)
Dimension 216
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.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 60 \)
Character field: \(\Q\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 504 216 288
Cusp forms 456 216 240
Eisenstein series 48 0 48

Trace form

\( 216q - 8q^{4} + O(q^{10}) \) \( 216q - 8q^{4} + 8q^{16} + 60q^{24} + 64q^{34} + 12q^{36} + 48q^{46} + 216q^{49} - 84q^{54} + 96q^{61} - 80q^{64} + 92q^{66} + 48q^{69} + 48q^{76} + 16q^{81} + 72q^{94} - 44q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database