Properties

Label 2100.2.n
Level 2100
Weight 2
Character orbit n
Rep. character \(\chi_{2100}(1751,\cdot)\)
Character field \(\Q\)
Dimension 228
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.n (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
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 504 228 276
Cusp forms 456 228 228
Eisenstein series 48 0 48

Trace form

\( 228q + 4q^{4} - 6q^{6} - 4q^{9} + O(q^{10}) \) \( 228q + 4q^{4} - 6q^{6} - 4q^{9} - 6q^{12} - 20q^{16} + 20q^{18} - 2q^{24} + 8q^{28} - 16q^{33} - 32q^{34} + 32q^{36} + 16q^{37} - 10q^{42} + 48q^{46} - 34q^{48} - 228q^{49} - 12q^{52} - 10q^{54} + 32q^{57} - 56q^{58} + 16q^{61} + 52q^{64} - 40q^{66} + 24q^{69} + 8q^{72} + 24q^{73} - 12q^{76} + 72q^{78} + 12q^{81} + 24q^{82} - 14q^{84} + 80q^{88} + 72q^{93} + 152q^{94} + 74q^{96} - 24q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database