Properties

Label 2100.2.t
Level 2100
Weight 2
Character orbit t
Rep. character \(\chi_{2100}(43,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 216
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.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1008 216 792
Cusp forms 912 216 696
Eisenstein series 96 0 96

Trace form

\( 216q - 16q^{6} + O(q^{10}) \) \( 216q - 16q^{6} - 16q^{12} - 8q^{13} - 16q^{16} - 40q^{17} + 24q^{22} + 40q^{32} + 16q^{36} + 8q^{37} + 56q^{38} + 56q^{46} + 16q^{52} + 8q^{53} + 24q^{56} - 32q^{58} - 128q^{61} - 40q^{62} + 56q^{68} + 104q^{73} + 128q^{76} - 24q^{78} - 216q^{81} + 96q^{82} + 104q^{86} + 8q^{88} + 40q^{92} - 16q^{93} - 64q^{96} + 40q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database