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Properties

Label 1400.2.bk
Level $1400$
Weight $2$
Character orbit 1400.bk
Rep. character $\chi_{1400}(451,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $292$
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.bk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 504 316 188
Cusp forms 456 292 164
Eisenstein series 48 24 24

Trace form

\( 292 q + 2 q^{2} + 6 q^{3} + 2 q^{4} + 8 q^{8} + 136 q^{9} + O(q^{10}) \) \( 292 q + 2 q^{2} + 6 q^{3} + 2 q^{4} + 8 q^{8} + 136 q^{9} - 10 q^{11} - 12 q^{12} - 4 q^{14} + 6 q^{16} + 6 q^{17} - 6 q^{18} + 6 q^{19} + 24 q^{22} - 6 q^{24} + 12 q^{26} - 8 q^{28} + 22 q^{32} + 6 q^{33} + 28 q^{36} - 36 q^{38} + 28 q^{42} + 16 q^{43} - 6 q^{44} + 14 q^{46} - 4 q^{49} + 26 q^{51} + 60 q^{52} + 30 q^{54} - 6 q^{56} + 4 q^{57} - 24 q^{58} - 42 q^{59} + 8 q^{64} - 12 q^{66} + 10 q^{67} + 36 q^{68} + 40 q^{72} + 30 q^{73} - 38 q^{74} + 12 q^{78} - 102 q^{81} - 12 q^{82} + 82 q^{84} - 68 q^{86} - 22 q^{88} - 18 q^{89} + 8 q^{91} + 48 q^{92} - 78 q^{94} + 30 q^{96} - 4 q^{98} - 104 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)