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Properties

Label 1400.2.bg
Level $1400$
Weight $2$
Character orbit 1400.bg
Rep. character $\chi_{1400}(149,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $280$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.bg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1400, [\chi])\).

Total New Old
Modular forms 504 296 208
Cusp forms 456 280 176
Eisenstein series 48 16 32

Trace form

\( 280 q + 2 q^{4} - 16 q^{6} - 128 q^{9} + O(q^{10}) \) \( 280 q + 2 q^{4} - 16 q^{6} - 128 q^{9} - 10 q^{14} - 10 q^{16} - 4 q^{24} + 18 q^{26} + 20 q^{31} - 48 q^{34} - 44 q^{36} - 8 q^{39} - 16 q^{41} + 16 q^{44} + 20 q^{46} + 8 q^{49} - 6 q^{54} - 38 q^{56} + 8 q^{64} + 104 q^{66} - 80 q^{71} + 54 q^{74} - 60 q^{76} + 4 q^{79} - 116 q^{81} + 10 q^{84} - 12 q^{86} - 12 q^{89} + 18 q^{94} - 134 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1400, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1400, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)