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Properties

Label 2100.2.cy
Level $2100$
Weight $2$
Character orbit 2100.cy
Rep. character $\chi_{2100}(19,\cdot)$
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.cy (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

\( 1920 q - 60 q^{8} - 240 q^{9} + O(q^{10}) \) \( 1920 q - 60 q^{8} - 240 q^{9} - 18 q^{10} + 12 q^{14} - 4 q^{25} - 32 q^{30} + 90 q^{38} + 30 q^{40} - 20 q^{46} - 8 q^{49} - 132 q^{50} + 270 q^{52} + 36 q^{56} - 60 q^{58} - 2 q^{60} + 12 q^{64} + 42 q^{70} + 30 q^{72} + 44 q^{74} + 36 q^{80} + 240 q^{81} - 48 q^{84} + 32 q^{85} + 170 q^{88} + 180 q^{92} - 90 q^{96} - 280 q^{98} + O(q^{100}) \)

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

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