Properties

Label 2100.2.bj
Level 2100
Weight 2
Character orbit bj
Rep. character \(\chi_{2100}(451,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 304
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.bj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1008 304 704
Cusp forms 912 304 608
Eisenstein series 96 0 96

Trace form

\( 304q + 2q^{2} - 2q^{4} - 16q^{8} - 152q^{9} + O(q^{10}) \) \( 304q + 2q^{2} - 2q^{4} - 16q^{8} - 152q^{9} + 22q^{14} + 6q^{16} + 2q^{18} - 8q^{21} - 12q^{22} + 18q^{24} + 30q^{26} - 14q^{28} - 32q^{29} + 12q^{32} + 12q^{33} + 4q^{36} + 12q^{37} - 18q^{38} - 4q^{42} - 32q^{44} + 44q^{46} - 32q^{49} - 72q^{52} - 8q^{53} + 36q^{56} + 24q^{57} + 6q^{58} + 24q^{61} + 52q^{64} + 36q^{66} + 96q^{68} + 8q^{72} - 36q^{73} - 6q^{74} - 32q^{77} + 36q^{78} - 152q^{81} + 36q^{82} + 16q^{84} - 2q^{86} - 6q^{88} + 16q^{92} - 4q^{93} - 72q^{94} - 30q^{96} + 72q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database