Properties

Label 2850.2.r
Level $2850$
Weight $2$
Character orbit 2850.r
Rep. character $\chi_{2850}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
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.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 1248 120 1128
Cusp forms 1152 120 1032
Eisenstein series 96 0 96

Trace form

\( 120q + 60q^{4} + 60q^{9} + O(q^{10}) \) \( 120q + 60q^{4} + 60q^{9} - 32q^{11} - 8q^{14} - 60q^{16} + 8q^{19} + 4q^{21} + 32q^{26} + 16q^{29} + 8q^{31} - 16q^{34} - 60q^{36} - 8q^{39} + 8q^{41} - 16q^{44} - 80q^{46} - 96q^{49} + 8q^{51} - 16q^{56} - 16q^{59} - 12q^{61} - 120q^{64} + 16q^{69} - 80q^{71} - 24q^{74} + 28q^{76} + 4q^{79} - 60q^{81} + 8q^{84} + 16q^{86} + 80q^{89} + 68q^{91} - 16q^{99} + O(q^{100}) \)

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

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