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Properties

Label 1400.2.cp
Level $1400$
Weight $2$
Character orbit 1400.cp
Rep. character $\chi_{1400}(267,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1440$
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.cp (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1952 1440 512
Cusp forms 1888 1440 448
Eisenstein series 64 0 64

Trace form

\( 1440 q + O(q^{10}) \) \( 1440 q - 16 q^{10} + 16 q^{12} - 8 q^{17} + 28 q^{18} + 20 q^{20} + 36 q^{22} + 8 q^{25} + 4 q^{30} - 40 q^{32} - 96 q^{40} + 80 q^{42} + 64 q^{43} - 140 q^{44} - 180 q^{48} - 16 q^{52} + 260 q^{54} + 136 q^{58} - 20 q^{60} + 140 q^{62} + 8 q^{65} + 24 q^{68} - 40 q^{72} + 40 q^{73} - 112 q^{75} - 28 q^{78} + 20 q^{80} + 360 q^{81} - 104 q^{82} - 80 q^{83} - 32 q^{88} + 200 q^{89} - 136 q^{90} - 104 q^{92} - 320 q^{94} + 40 q^{96} + 8 q^{97} + O(q^{100}) \)

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

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