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Properties

Label 2100.2.n
Level $2100$
Weight $2$
Character orbit 2100.n
Rep. character $\chi_{2100}(1751,\cdot)$
Character field $\Q$
Dimension $228$
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.n (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 504 228 276
Cusp forms 456 228 228
Eisenstein series 48 0 48

Trace form

\( 228 q + 4 q^{4} - 6 q^{6} - 4 q^{9} + O(q^{10}) \) \( 228 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 6 q^{12} - 20 q^{16} + 20 q^{18} - 2 q^{24} + 8 q^{28} - 16 q^{33} - 32 q^{34} + 32 q^{36} + 16 q^{37} - 10 q^{42} + 48 q^{46} - 34 q^{48} - 228 q^{49} - 12 q^{52} - 10 q^{54} + 32 q^{57} - 56 q^{58} + 16 q^{61} + 52 q^{64} - 40 q^{66} + 24 q^{69} + 8 q^{72} + 24 q^{73} - 12 q^{76} + 72 q^{78} + 12 q^{81} + 24 q^{82} - 14 q^{84} + 80 q^{88} + 72 q^{93} + 152 q^{94} + 74 q^{96} - 24 q^{97} + O(q^{100}) \)

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

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