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Properties

Label 2100.2.bj
Level $2100$
Weight $2$
Character orbit 2100.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

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

Display 100 coefficients 10 coefficients

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

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