Properties

Label 2100.2.dn
Level 2100
Weight 2
Character orbit dn
Rep. character \(\chi_{2100}(67,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 3840
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.dn (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 700 \)
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 7808 3840 3968
Cusp forms 7552 3840 3712
Eisenstein series 256 0 256

Trace form

\( 3840q - 24q^{8} + O(q^{10}) \) \( 3840q - 24q^{8} + 44q^{28} - 8q^{33} - 48q^{38} - 20q^{40} + 20q^{42} + 32q^{48} + 288q^{50} - 104q^{52} + 40q^{58} + 20q^{60} + 144q^{62} + 120q^{64} + 44q^{68} + 80q^{70} + 12q^{72} - 16q^{73} + 48q^{77} + 48q^{78} + 36q^{80} - 480q^{81} - 4q^{82} + 160q^{84} + 96q^{85} - 140q^{88} - 96q^{90} + 72q^{92} + 64q^{93} + 320q^{97} + 416q^{98} + O(q^{100}) \)

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