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Properties

Label 1400.2.do
Level $1400$
Weight $2$
Character orbit 1400.do
Rep. character $\chi_{1400}(67,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3776$
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.do (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1400 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 3904 3904 0
Cusp forms 3776 3776 0
Eisenstein series 128 128 0

Trace form

\( 3776 q - 8 q^{2} - 16 q^{3} - 10 q^{4} - 24 q^{6} - 20 q^{8} - 20 q^{9} + O(q^{10}) \) \( 3776 q - 8 q^{2} - 16 q^{3} - 10 q^{4} - 24 q^{6} - 20 q^{8} - 20 q^{9} - 8 q^{10} - 12 q^{11} + 4 q^{12} - 20 q^{14} - 6 q^{16} - 16 q^{17} + 6 q^{18} - 20 q^{19} - 48 q^{20} - 40 q^{22} - 16 q^{25} - 16 q^{26} - 40 q^{27} + 14 q^{28} + 2 q^{30} - 28 q^{32} - 40 q^{33} - 40 q^{34} - 8 q^{35} + 8 q^{36} - 24 q^{38} + 12 q^{40} - 48 q^{41} - 50 q^{42} - 64 q^{43} - 10 q^{44} - 6 q^{46} - 76 q^{48} + 72 q^{50} - 32 q^{51} + 112 q^{52} - 10 q^{54} - 12 q^{56} - 40 q^{57} + 4 q^{58} - 20 q^{59} - 60 q^{60} - 96 q^{62} - 100 q^{64} - 16 q^{65} + 18 q^{66} + 8 q^{67} + 30 q^{68} - 84 q^{70} - 22 q^{72} - 16 q^{73} - 16 q^{75} - 32 q^{76} - 164 q^{78} + 30 q^{80} - 420 q^{81} - 84 q^{82} - 64 q^{83} + 140 q^{84} - 6 q^{86} - 66 q^{88} - 20 q^{89} - 284 q^{90} - 24 q^{91} - 84 q^{92} - 10 q^{94} - 6 q^{96} - 192 q^{97} + 170 q^{98} + O(q^{100}) \)

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.