Properties

Label 2100.2.ct
Level 2100
Weight 2
Character orbit ct
Rep. character \(\chi_{2100}(113,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 480
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.ct (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
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 3936 480 3456
Cusp forms 3744 480 3264
Eisenstein series 192 0 192

Trace form

\( 480q + 4q^{3} + O(q^{10}) \) \( 480q + 4q^{3} - 24q^{13} - 8q^{15} - 40q^{19} - 88q^{25} - 8q^{27} + 20q^{33} - 32q^{37} + 40q^{39} + 8q^{43} - 20q^{45} + 8q^{55} + 28q^{57} + 32q^{63} + 104q^{67} + 80q^{73} + 28q^{75} + 80q^{79} - 40q^{81} + 184q^{85} + 120q^{87} + 104q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database