Properties

Label 2850.2.bp
Level $2850$
Weight $2$
Character orbit 2850.bp
Rep. character $\chi_{2850}(37,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $800$
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.bp (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 4864 800 4064
Cusp forms 4736 800 3936
Eisenstein series 128 0 128

Trace form

\( 800q - 8q^{5} + 8q^{7} + O(q^{10}) \) \( 800q - 8q^{5} + 8q^{7} + 200q^{16} - 32q^{17} + 40q^{19} + 120q^{23} + 24q^{25} + 8q^{28} - 64q^{30} + 32q^{35} - 200q^{36} + 16q^{38} + 120q^{43} - 120q^{47} + 80q^{55} - 8q^{57} + 32q^{62} - 8q^{63} + 8q^{68} + 24q^{73} - 64q^{77} + 8q^{80} + 200q^{81} + 32q^{82} - 88q^{85} + 64q^{87} + 40q^{92} - 64q^{93} + 136q^{95} + O(q^{100}) \)

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

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