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Properties

Label 1400.2.s
Level $1400$
Weight $2$
Character orbit 1400.s
Rep. character $\chi_{1400}(293,\cdot)$
Character field $\Q(\zeta_{4})$
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.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q(i)\)
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

\( 280 q + 4 q^{2} + 4 q^{7} + 16 q^{8} + O(q^{10}) \) \( 280 q + 4 q^{2} + 4 q^{7} + 16 q^{8} + 24 q^{16} + 8 q^{18} - 4 q^{22} + 8 q^{23} + 4 q^{28} + 24 q^{32} + 24 q^{36} - 40 q^{42} + 4 q^{46} - 76 q^{56} - 16 q^{57} + 68 q^{58} - 12 q^{63} + 112 q^{71} - 80 q^{72} + 132 q^{78} - 168 q^{81} + 180 q^{86} - 48 q^{88} + 24 q^{92} - 40 q^{98} + O(q^{100}) \)

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

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