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Properties

Label 1400.2.ch
Level $1400$
Weight $2$
Character orbit 1400.ch
Rep. character $\chi_{1400}(107,\cdot)$
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.ch (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

\( 560 q + 2 q^{2} + 4 q^{3} - 16 q^{6} + 20 q^{8} + O(q^{10}) \) \( 560 q + 2 q^{2} + 4 q^{3} - 16 q^{6} + 20 q^{8} - 8 q^{11} + 14 q^{12} - 20 q^{16} + 4 q^{17} + 16 q^{18} + 28 q^{26} + 40 q^{27} + 34 q^{28} - 18 q^{32} - 20 q^{33} - 48 q^{36} + 16 q^{38} - 32 q^{41} - 30 q^{42} + 16 q^{43} + 8 q^{46} - 36 q^{48} - 8 q^{51} + 32 q^{52} + 80 q^{56} + 40 q^{57} + 14 q^{58} - 56 q^{62} + 36 q^{66} + 28 q^{67} + 40 q^{68} + 48 q^{72} + 4 q^{73} + 144 q^{76} - 184 q^{78} + 176 q^{81} - 74 q^{82} + 16 q^{83} + 40 q^{86} + 64 q^{88} - 80 q^{91} - 44 q^{92} + 196 q^{96} + 48 q^{97} - 70 q^{98} + O(q^{100}) \)

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

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