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

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

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

\( S_{2}^{\mathrm{old}}(2850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1425, [\chi])\)\(^{\oplus 2}\)