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Properties

Label 2100.2.br
Level $2100$
Weight $2$
Character orbit 2100.br
Rep. character $\chi_{2100}(71,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1440$
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.br (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 300 \)
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 1440 512
Cusp forms 1888 1440 448
Eisenstein series 64 0 64

Trace form

\( 1440 q + O(q^{10}) \) \( 1440 q - 8 q^{10} + 24 q^{16} + 28 q^{18} + 16 q^{22} + 28 q^{24} - 4 q^{30} - 30 q^{36} - 48 q^{37} + 8 q^{40} + 30 q^{42} - 24 q^{45} + 50 q^{48} - 1440 q^{49} + 16 q^{52} + 78 q^{54} + 16 q^{57} + 36 q^{58} + 92 q^{60} - 32 q^{61} - 24 q^{64} + 90 q^{66} + 48 q^{69} + 12 q^{70} + 40 q^{72} - 78 q^{78} + 24 q^{81} - 64 q^{82} + 72 q^{85} + 76 q^{88} + 80 q^{90} + 48 q^{93} - 188 q^{94} + 76 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)