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Properties

Label 1400.2.bt
Level $1400$
Weight $2$
Character orbit 1400.bt
Rep. character $\chi_{1400}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $720$
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.bt (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 976 720 256
Cusp forms 944 720 224
Eisenstein series 32 0 32

Trace form

\( 720 q - 180 q^{9} + O(q^{10}) \) \( 720 q - 180 q^{9} + 8 q^{10} + 24 q^{16} + 24 q^{20} + 50 q^{22} + 28 q^{24} - 4 q^{25} + 20 q^{26} - 4 q^{30} - 30 q^{36} - 70 q^{38} + 32 q^{39} + 34 q^{40} + 8 q^{41} - 50 q^{42} + 42 q^{44} + 130 q^{48} - 720 q^{49} + 82 q^{50} - 78 q^{54} + 32 q^{55} - 10 q^{58} - 50 q^{62} + 24 q^{64} - 76 q^{65} - 106 q^{66} + 12 q^{70} - 56 q^{71} + 28 q^{74} - 20 q^{76} + 130 q^{78} - 40 q^{79} - 64 q^{80} - 180 q^{81} + 80 q^{86} - 60 q^{88} - 60 q^{89} + 52 q^{90} - 100 q^{92} - 104 q^{94} + 160 q^{95} - 56 q^{96} + O(q^{100}) \)

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

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