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Properties

Label 1400.2.w
Level $1400$
Weight $2$
Character orbit 1400.w
Rep. character $\chi_{1400}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $216$
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.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 504 216 288
Cusp forms 456 216 240
Eisenstein series 48 0 48

Trace form

\( 216 q - 16 q^{6} + O(q^{10}) \) \( 216 q - 16 q^{6} + 16 q^{12} + 16 q^{16} - 8 q^{17} + 28 q^{18} + 36 q^{22} + 64 q^{26} - 40 q^{32} - 128 q^{36} - 20 q^{42} + 64 q^{43} - 36 q^{46} + 80 q^{48} + 64 q^{51} - 16 q^{52} - 12 q^{56} - 4 q^{58} + 40 q^{62} - 64 q^{66} + 24 q^{68} - 40 q^{72} + 40 q^{73} + 16 q^{76} - 28 q^{78} - 216 q^{81} - 24 q^{82} - 80 q^{83} - 76 q^{86} + 88 q^{88} + 96 q^{92} - 128 q^{96} + 8 q^{97} + O(q^{100}) \)

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

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