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Properties

Label 2800.2.ef
Level $2800$
Weight $2$
Character orbit 2800.ef
Rep. character $\chi_{2800}(531,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $3808$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2800.ef (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2800 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2800, [\chi])\).

Total New Old
Modular forms 3872 3872 0
Cusp forms 3808 3808 0
Eisenstein series 64 64 0

Trace form

\( 3808 q - 12 q^{2} - 12 q^{4} - 32 q^{7} - 48 q^{8} + O(q^{10}) \) \( 3808 q - 12 q^{2} - 12 q^{4} - 32 q^{7} - 48 q^{8} - 12 q^{11} - 18 q^{14} - 12 q^{16} - 48 q^{18} + 12 q^{21} - 12 q^{22} - 24 q^{23} - 30 q^{28} - 12 q^{29} - 44 q^{30} - 32 q^{32} + 44 q^{35} + 16 q^{36} - 12 q^{37} - 24 q^{39} + 70 q^{42} - 32 q^{43} - 12 q^{44} + 4 q^{46} - 32 q^{49} - 36 q^{50} - 56 q^{51} - 12 q^{53} - 48 q^{56} - 76 q^{58} - 88 q^{60} - 48 q^{64} - 32 q^{65} - 84 q^{67} + 60 q^{70} - 24 q^{71} - 76 q^{72} - 120 q^{74} - 48 q^{77} + 204 q^{78} + 864 q^{81} - 40 q^{84} - 36 q^{85} - 52 q^{86} + 120 q^{88} + 36 q^{91} - 88 q^{92} - 8 q^{93} - 74 q^{98} - 128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2800, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.