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Properties

Label 1400.2.cl
Level $1400$
Weight $2$
Character orbit 1400.cl
Rep. character $\chi_{1400}(157,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $560$
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.cl (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1008 592 416
Cusp forms 912 560 352
Eisenstein series 96 32 64

Trace form

\( 560 q + 2 q^{2} + 8 q^{7} - 4 q^{8} + O(q^{10}) \) \( 560 q + 2 q^{2} + 8 q^{7} - 4 q^{8} + 6 q^{12} + 12 q^{16} + 12 q^{17} + 16 q^{18} + 16 q^{22} + 4 q^{23} - 12 q^{26} + 50 q^{28} - 24 q^{31} - 18 q^{32} + 12 q^{33} - 48 q^{36} + 24 q^{38} + 10 q^{42} - 16 q^{46} + 84 q^{47} - 72 q^{52} + 16 q^{56} + 40 q^{57} - 2 q^{58} + 24 q^{63} + 60 q^{66} - 60 q^{68} - 160 q^{71} - 52 q^{72} + 12 q^{73} + 24 q^{78} + 240 q^{81} + 54 q^{82} + 72 q^{86} + 48 q^{87} - 60 q^{88} - 12 q^{92} + 156 q^{96} + 130 q^{98} + O(q^{100}) \)

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

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