Properties

Label 2850.2.bf
Level $2850$
Weight $2$
Character orbit 2850.bf
Rep. character $\chi_{2850}(943,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $240$
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.bf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 2496 240 2256
Cusp forms 2304 240 2064
Eisenstein series 192 0 192

Trace form

\( 240q + 16q^{7} + O(q^{10}) \) \( 240q + 16q^{7} - 32q^{11} + 120q^{16} - 8q^{17} + 24q^{21} - 24q^{22} - 8q^{23} - 64q^{26} - 8q^{28} + 24q^{33} - 120q^{36} - 16q^{38} + 48q^{41} + 16q^{43} + 8q^{47} - 72q^{53} + 32q^{57} + 8q^{61} + 16q^{62} + 8q^{63} + 72q^{67} + 16q^{68} + 48q^{73} - 40q^{76} + 64q^{77} - 48q^{78} + 120q^{81} + 16q^{82} + 128q^{83} + 96q^{86} - 32q^{87} + 312q^{91} + 8q^{92} - 16q^{93} + 24q^{97} + 96q^{98} + O(q^{100}) \)

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

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