Properties

Label 2100.2.dr
Level 2100
Weight 2
Character orbit dr
Rep. character \(\chi_{2100}(73,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 640
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.dr (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 7872 640 7232
Cusp forms 7488 640 6848
Eisenstein series 384 0 384

Trace form

\( 640q + 12q^{5} + O(q^{10}) \) \( 640q + 12q^{5} - 8q^{15} + 24q^{23} + 4q^{25} - 80q^{29} - 12q^{33} - 40q^{35} - 20q^{37} - 136q^{43} - 12q^{47} + 120q^{53} + 16q^{57} + 240q^{59} + 12q^{63} + 52q^{65} + 60q^{73} + 48q^{75} + 84q^{77} - 80q^{81} + 8q^{85} + 48q^{87} + 32q^{93} - 44q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database