Properties

Label 2850.2.i
Level $2850$
Weight $2$
Character orbit 2850.i
Rep. character $\chi_{2850}(2101,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $124$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 1248 124 1124
Cusp forms 1152 124 1028
Eisenstein series 96 0 96

Trace form

\( 124q + 2q^{3} - 62q^{4} + 12q^{7} - 62q^{9} + O(q^{10}) \) \( 124q + 2q^{3} - 62q^{4} + 12q^{7} - 62q^{9} - 4q^{12} - 6q^{13} + 12q^{14} - 62q^{16} - 12q^{17} - 24q^{19} - 14q^{21} + 4q^{22} + 8q^{23} + 24q^{26} - 4q^{27} - 6q^{28} + 12q^{29} + 4q^{31} + 8q^{33} - 12q^{34} - 62q^{36} - 12q^{37} - 8q^{38} + 28q^{39} - 4q^{42} - 14q^{43} + 32q^{46} - 4q^{47} + 2q^{48} + 120q^{49} - 4q^{51} - 6q^{52} - 24q^{56} + 6q^{57} + 8q^{58} - 28q^{59} - 6q^{61} + 12q^{62} - 6q^{63} + 124q^{64} + 4q^{66} + 2q^{67} + 24q^{68} + 16q^{69} - 2q^{73} + 12q^{74} + 18q^{76} - 48q^{77} + 12q^{78} + 22q^{79} - 62q^{81} + 16q^{82} + 24q^{83} + 28q^{84} + 24q^{87} - 8q^{88} - 36q^{89} + 18q^{91} + 8q^{92} - 18q^{93} + 48q^{94} + 28q^{97} - 8q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1425, [\chi])\)\(^{\oplus 2}\)