Properties

Label 2100.2.cs
Level 2100
Weight 2
Character orbit cs
Rep. character \(\chi_{2100}(127,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 1440
Sturm bound 960

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.cs (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 3904 1440 2464
Cusp forms 3776 1440 2336
Eisenstein series 128 0 128

Trace form

\( 1440q + O(q^{10}) \) \( 1440q - 16q^{10} - 16q^{12} - 8q^{13} - 40q^{17} + 40q^{20} + 24q^{22} - 40q^{25} + 16q^{30} + 40q^{32} + 8q^{37} + 56q^{38} + 144q^{40} + 280q^{44} + 8q^{45} + 40q^{50} + 16q^{52} + 8q^{53} + 248q^{58} + 160q^{62} + 40q^{65} + 56q^{68} + 104q^{73} - 24q^{78} + 80q^{80} + 360q^{81} + 16q^{82} + 32q^{85} - 112q^{88} + 520q^{89} - 360q^{92} + 64q^{93} - 80q^{94} + 40q^{96} + 40q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database