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Properties

Label 1400.2.bb
Level $1400$
Weight $2$
Character orbit 1400.bb
Rep. character $\chi_{1400}(299,\cdot)$
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.bb (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

\( 280 q + 2 q^{4} - 128 q^{9} + O(q^{10}) \) \( 280 q + 2 q^{4} - 128 q^{9} - 4 q^{11} + 30 q^{14} + 6 q^{16} + 12 q^{19} + 24 q^{24} - 18 q^{26} + 36 q^{36} - 16 q^{44} - 24 q^{46} + 8 q^{49} - 28 q^{51} - 126 q^{54} + 86 q^{56} + 108 q^{59} + 8 q^{64} - 60 q^{66} + 10 q^{74} - 84 q^{81} + 94 q^{84} - 36 q^{86} + 60 q^{89} - 32 q^{91} + 78 q^{94} - 150 q^{96} - 32 q^{99} + O(q^{100}) \)

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

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