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Properties

Label 1400.2.br
Level $1400$
Weight $2$
Character orbit 1400.br
Rep. character $\chi_{1400}(139,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $944$
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.br (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1400 \)
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 976 976 0
Cusp forms 944 944 0
Eisenstein series 32 32 0

Trace form

\( 944 q - 10 q^{2} - 6 q^{4} - 40 q^{8} - 240 q^{9} + O(q^{10}) \) \( 944 q - 10 q^{2} - 6 q^{4} - 40 q^{8} - 240 q^{9} - 12 q^{11} - 15 q^{14} - 6 q^{16} - 10 q^{22} - 16 q^{25} - 25 q^{28} - 62 q^{30} + 44 q^{35} - 8 q^{36} + 25 q^{42} + 10 q^{44} - 38 q^{46} - 16 q^{49} + 76 q^{50} - 8 q^{51} - 42 q^{56} + 50 q^{58} + 28 q^{60} - 36 q^{65} - 140 q^{67} - 10 q^{70} + 170 q^{72} - 52 q^{74} + 20 q^{78} - 192 q^{81} - 46 q^{84} - 14 q^{86} - 180 q^{88} + 36 q^{91} + 80 q^{92} - 85 q^{98} + 64 q^{99} + O(q^{100}) \)

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.