Properties

Label 2100.2.w
Level 2100
Weight 2
Character orbit w
Rep. character \(\chi_{2100}(1007,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 560
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.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 420 \)
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 592 416
Cusp forms 912 560 352
Eisenstein series 96 32 64

Trace form

\( 560q + O(q^{10}) \) \( 560q - 16q^{16} + 12q^{18} + 8q^{21} + 24q^{22} + 36q^{28} + 24q^{36} + 16q^{37} + 16q^{42} - 16q^{46} + 32q^{58} + 16q^{72} - 116q^{78} + 144q^{81} + 96q^{88} + 32q^{93} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database