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Properties

Label 1400.2.h
Level $1400$
Weight $2$
Character orbit 1400.h
Rep. character $\chi_{1400}(251,\cdot)$
Character field $\Q$
Dimension $146$
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.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 252 158 94
Cusp forms 228 146 82
Eisenstein series 24 12 12

Trace form

\( 146 q + q^{2} + q^{4} - 5 q^{8} - 130 q^{9} + O(q^{10}) \) \( 146 q + q^{2} + q^{4} - 5 q^{8} - 130 q^{9} - 8 q^{11} - 5 q^{14} - 3 q^{16} + 15 q^{18} - 13 q^{28} + 11 q^{32} - 61 q^{36} - 40 q^{42} + 8 q^{43} + 54 q^{44} - 8 q^{46} + 10 q^{49} + 16 q^{51} - 33 q^{56} + 8 q^{57} - 24 q^{58} - 5 q^{64} - 40 q^{67} + 65 q^{72} - 34 q^{74} + 36 q^{78} + 90 q^{81} - 76 q^{84} - 22 q^{86} + 52 q^{88} + 16 q^{91} + 42 q^{92} + 61 q^{98} + 56 q^{99} + O(q^{100}) \)

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

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