Properties

Label 2100.2.bw
Level 2100
Weight 2
Character orbit bw
Rep. character \(\chi_{2100}(139,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 960
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.bw (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 700 \)
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 960 992
Cusp forms 1888 960 928
Eisenstein series 64 0 64

Trace form

\( 960q + 60q^{8} + 240q^{9} + O(q^{10}) \) \( 960q + 60q^{8} + 240q^{9} - 12q^{14} - 8q^{25} - 64q^{30} - 40q^{46} + 8q^{49} + 132q^{50} - 36q^{56} + 60q^{58} + 32q^{60} + 60q^{64} + 60q^{72} + 88q^{74} - 240q^{81} - 24q^{84} - 56q^{85} + 160q^{88} - 180q^{92} - 140q^{98} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database