Properties

Label 2100.2.da
Level 2100
Weight 2
Character orbit da
Rep. character \(\chi_{2100}(31,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 1920
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.da (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 700 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 3904 1920 1984
Cusp forms 3776 1920 1856
Eisenstein series 128 0 128

Trace form

\( 1920q + 36q^{8} + 240q^{9} + O(q^{10}) \) \( 1920q + 36q^{8} + 240q^{9} + 18q^{10} + 12q^{14} + 4q^{25} - 20q^{28} + 32q^{30} + 24q^{33} + 54q^{38} + 30q^{40} - 20q^{42} + 20q^{46} - 8q^{49} - 156q^{50} + 162q^{52} - 36q^{56} + 52q^{58} + 22q^{60} + 12q^{64} + 132q^{68} - 34q^{70} - 18q^{72} + 44q^{74} - 48q^{77} + 48q^{78} + 72q^{80} + 240q^{81} + 60q^{82} - 48q^{84} + 64q^{85} - 30q^{88} - 108q^{92} + 64q^{93} + 90q^{96} - 136q^{98} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database