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Properties

Label 2100.2.bl
Level $2100$
Weight $2$
Character orbit 2100.bl
Rep. character $\chi_{2100}(199,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $288$
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.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
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 288 720
Cusp forms 912 288 624
Eisenstein series 96 0 96

Trace form

\( 288 q + 144 q^{9} + O(q^{10}) \) \( 288 q + 144 q^{9} - 20 q^{14} + 16 q^{16} + 28 q^{44} - 8 q^{46} + 24 q^{49} + 68 q^{56} + 96 q^{64} + 72 q^{66} + 56 q^{74} - 144 q^{81} + 8 q^{84} + 4 q^{86} + 72 q^{94} + 60 q^{96} + O(q^{100}) \)

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

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