Properties

Label 2100.2.ch
Level 2100
Weight 2
Character orbit ch
Rep. character \(\chi_{2100}(143,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 1120
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.ch (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 420 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 2016 1184 832
Cusp forms 1824 1120 704
Eisenstein series 192 64 128

Trace form

\( 1120q + O(q^{10}) \) \( 1120q + 6q^{12} - 8q^{16} - 6q^{18} - 32q^{21} + 24q^{28} + 12q^{33} - 48q^{36} + 8q^{37} + 26q^{42} - 8q^{46} + 60q^{52} + 72q^{57} + 52q^{58} - 48q^{61} + 60q^{66} + 38q^{72} + 24q^{73} + 56q^{78} + 72q^{81} + 96q^{82} + 12q^{88} - 20q^{93} - 180q^{96} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database