Properties

Label 2100.2.bt
Level 2100
Weight 2
Character orbit bt
Rep. character \(\chi_{2100}(239,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 1440
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.bt (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 300 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1952 1440 512
Cusp forms 1888 1440 448
Eisenstein series 64 0 64

Trace form

\( 1440q + O(q^{10}) \) \( 1440q - 8q^{10} - 24q^{16} + 28q^{24} + 24q^{30} + 30q^{36} + 80q^{37} + 8q^{40} + 50q^{42} + 24q^{45} + 130q^{48} + 1440q^{49} + 78q^{54} - 60q^{58} - 72q^{60} + 32q^{61} - 24q^{64} - 90q^{66} + 48q^{69} - 12q^{70} + 130q^{78} - 24q^{81} + 56q^{85} - 60q^{88} + 56q^{90} - 148q^{94} - 76q^{96} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database