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Properties

Label 2100.2.bw
Level $2100$
Weight $2$
Character orbit 2100.bw
Rep. character $\chi_{2100}(139,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $960$
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.bw (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 700 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1952 960 992
Cusp forms 1888 960 928
Eisenstein series 64 0 64

Trace form

\( 960 q + 60 q^{8} + 240 q^{9} + O(q^{10}) \) \( 960 q + 60 q^{8} + 240 q^{9} - 12 q^{14} - 8 q^{25} - 64 q^{30} - 40 q^{46} + 8 q^{49} + 132 q^{50} - 36 q^{56} + 60 q^{58} + 32 q^{60} + 60 q^{64} + 60 q^{72} + 88 q^{74} - 240 q^{81} - 24 q^{84} - 56 q^{85} + 160 q^{88} - 180 q^{92} - 140 q^{98} + O(q^{100}) \)

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

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