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Properties

Label 2850.2.n
Level $2850$
Weight $2$
Character orbit 2850.n
Rep. character $\chi_{2850}(571,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $368$
Sturm bound $1200$

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Defining parameters

Level: \( N \) \(=\) \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2850.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2850, [\chi])\).

Total New Old
Modular forms 2432 368 2064
Cusp forms 2368 368 2000
Eisenstein series 64 0 64

Trace form

\( 368 q - 4 q^{2} - 92 q^{4} - 8 q^{5} - 4 q^{6} - 16 q^{7} - 4 q^{8} - 92 q^{9} + O(q^{10}) \) \( 368 q - 4 q^{2} - 92 q^{4} - 8 q^{5} - 4 q^{6} - 16 q^{7} - 4 q^{8} - 92 q^{9} - 8 q^{10} + 12 q^{11} - 8 q^{13} - 4 q^{15} - 92 q^{16} + 4 q^{17} + 16 q^{18} - 4 q^{19} + 12 q^{20} - 8 q^{22} + 12 q^{23} + 16 q^{24} - 12 q^{25} - 24 q^{26} + 4 q^{28} - 24 q^{29} + 12 q^{31} + 16 q^{32} - 8 q^{33} + 36 q^{34} - 12 q^{35} - 92 q^{36} - 36 q^{37} - 8 q^{40} + 48 q^{41} + 12 q^{42} - 8 q^{43} - 8 q^{44} - 8 q^{45} - 56 q^{47} + 416 q^{49} - 20 q^{50} - 8 q^{52} + 60 q^{53} - 4 q^{54} - 40 q^{55} - 48 q^{58} + 16 q^{60} - 56 q^{61} + 72 q^{62} + 4 q^{63} - 92 q^{64} - 52 q^{65} - 16 q^{66} - 32 q^{67} - 16 q^{68} + 52 q^{70} - 4 q^{72} + 24 q^{73} - 56 q^{74} - 32 q^{75} + 16 q^{76} - 112 q^{77} + 40 q^{79} - 8 q^{80} - 92 q^{81} + 120 q^{82} + 12 q^{83} + 48 q^{85} - 48 q^{86} - 56 q^{87} + 12 q^{88} + 36 q^{89} - 8 q^{90} - 8 q^{91} - 8 q^{92} - 32 q^{93} - 4 q^{95} - 4 q^{96} - 92 q^{97} - 36 q^{98} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2850, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)