Properties

Label 2100.2.do
Level 2100
Weight 2
Character orbit do
Rep. character \(\chi_{2100}(47,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 7552
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.do (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2100 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 7808 7808 0
Cusp forms 7552 7552 0
Eisenstein series 256 256 0

Trace form

\( 7552q - 20q^{4} - 20q^{9} + O(q^{10}) \) \( 7552q - 20q^{4} - 20q^{9} - 48q^{10} - 24q^{12} - 12q^{16} - 16q^{18} - 24q^{21} - 80q^{22} - 32q^{25} - 16q^{28} + 22q^{30} - 48q^{33} + 8q^{36} - 32q^{37} + 12q^{40} + 6q^{42} - 48q^{45} - 12q^{46} - 30q^{54} - 8q^{57} + 32q^{58} + 80q^{60} - 72q^{61} - 80q^{64} - 90q^{66} + 64q^{70} + 28q^{72} - 96q^{73} - 44q^{78} - 12q^{81} + 36q^{82} - 20q^{84} - 128q^{85} + 112q^{88} - 40q^{93} - 60q^{94} - 18q^{96} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database