Properties

Label 2100.2.cl
Level 2100
Weight 2
Character orbit cl
Rep. character \(\chi_{2100}(557,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 192
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.cl (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 2064 192 1872
Cusp forms 1776 192 1584
Eisenstein series 288 0 288

Trace form

\( 192q - 4q^{7} + O(q^{10}) \) \( 192q - 4q^{7} - 24q^{21} - 8q^{31} - 10q^{33} + 8q^{37} - 32q^{43} + 24q^{51} - 60q^{57} + 76q^{61} - 26q^{63} + 16q^{67} + 8q^{73} + 16q^{81} + 38q^{87} + 84q^{91} + 6q^{93} + 40q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database