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Properties

Label 1400.2.b
Level $1400$
Weight $2$
Character orbit 1400.b
Rep. character $\chi_{1400}(701,\cdot)$
Character field $\Q$
Dimension $114$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 252 114 138
Cusp forms 228 114 114
Eisenstein series 24 0 24

Trace form

\( 114 q - q^{2} + 5 q^{4} + 10 q^{6} - 2 q^{7} - 7 q^{8} - 114 q^{9} + O(q^{10}) \) \( 114 q - q^{2} + 5 q^{4} + 10 q^{6} - 2 q^{7} - 7 q^{8} - 114 q^{9} - 2 q^{12} + q^{14} + 9 q^{16} + 4 q^{17} + 13 q^{18} - 2 q^{22} - 8 q^{23} - 6 q^{24} - 32 q^{26} - 5 q^{28} + 16 q^{31} + 9 q^{32} + 8 q^{33} + 22 q^{34} - 9 q^{36} - 38 q^{38} + 40 q^{39} - 12 q^{41} + 10 q^{42} - 20 q^{44} - 14 q^{46} - 34 q^{48} + 114 q^{49} - 20 q^{52} + 8 q^{54} + 13 q^{56} - 8 q^{57} + 32 q^{58} + 48 q^{62} + 10 q^{63} + 47 q^{64} - 80 q^{66} + 50 q^{68} + 24 q^{71} - 9 q^{72} + 20 q^{73} + 54 q^{74} - 22 q^{76} + 12 q^{78} - 56 q^{79} + 122 q^{81} + 14 q^{82} - 14 q^{84} + 8 q^{86} - 80 q^{87} - 2 q^{88} + 20 q^{89} - 8 q^{92} + 44 q^{94} - 46 q^{96} + 4 q^{97} - q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)