Properties

Label 2100.2.dk
Level 2100
Weight 2
Character orbit dk
Rep. character \(\chi_{2100}(53,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 1280
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.dk (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
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 1280 6592
Cusp forms 7488 1280 6208
Eisenstein series 384 0 384

Trace form

\( 1280q - 4q^{7} + O(q^{10}) \) \( 1280q - 4q^{7} - 12q^{15} + 8q^{25} - 10q^{33} + 8q^{37} + 40q^{39} - 32q^{43} - 70q^{45} + 16q^{55} + 100q^{57} + 24q^{63} + 16q^{67} + 140q^{69} + 8q^{73} - 40q^{75} + 40q^{85} + 38q^{87} + 6q^{93} + 80q^{97} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database