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Properties

Label 1400.2.dk
Level $1400$
Weight $2$
Character orbit 1400.dk
Rep. character $\chi_{1400}(117,\cdot)$
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.dk (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

\( 3776 q - 8 q^{2} - 10 q^{4} - 32 q^{7} - 44 q^{8} - 20 q^{9} + O(q^{10}) \) \( 3776 q - 8 q^{2} - 10 q^{4} - 32 q^{7} - 44 q^{8} - 20 q^{9} - 24 q^{10} - 24 q^{12} - 20 q^{14} - 64 q^{15} - 6 q^{16} - 48 q^{17} + 6 q^{18} - 24 q^{22} - 16 q^{23} - 16 q^{25} - 48 q^{26} + 30 q^{28} - 18 q^{30} - 36 q^{31} - 28 q^{32} - 48 q^{33} + 8 q^{36} - 96 q^{38} - 20 q^{39} - 84 q^{40} - 10 q^{42} - 10 q^{44} - 6 q^{46} + 24 q^{47} + 152 q^{50} + 168 q^{52} - 30 q^{54} - 12 q^{56} - 40 q^{57} - 12 q^{58} + 44 q^{60} - 16 q^{63} - 100 q^{64} - 16 q^{65} + 54 q^{66} - 90 q^{68} + 92 q^{70} - 48 q^{71} - 122 q^{72} - 48 q^{73} + 44 q^{78} - 20 q^{79} - 78 q^{80} - 420 q^{81} + 24 q^{82} - 180 q^{84} - 6 q^{86} - 12 q^{87} + 50 q^{88} - 60 q^{89} - 52 q^{92} - 30 q^{94} - 18 q^{96} - 190 q^{98} + O(q^{100}) \)

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.