Properties

Label 2100.2.ci
Level 2100
Weight 2
Character orbit ci
Rep. character \(\chi_{2100}(907,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 576
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.ci (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
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 2016 576 1440
Cusp forms 1824 576 1248
Eisenstein series 192 0 192

Trace form

\( 576q - 24q^{8} + O(q^{10}) \) \( 576q - 24q^{8} - 32q^{16} + 64q^{26} + 44q^{28} - 8q^{33} + 12q^{38} + 64q^{41} + 20q^{42} + 24q^{46} + 32q^{48} + 76q^{52} + 64q^{56} + 40q^{58} + 144q^{62} + 48q^{66} + 44q^{68} + 12q^{72} - 16q^{73} + 192q^{76} + 48q^{77} + 48q^{78} + 288q^{81} - 4q^{82} + 8q^{86} - 20q^{88} + 72q^{92} - 16q^{93} - 80q^{97} - 144q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database