Properties

Label 2850.2.br
Level $2850$
Weight $2$
Character orbit 2850.br
Rep. character $\chi_{2850}(77,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1440$
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.br (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
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 1440 3424
Cusp forms 4736 1440 3296
Eisenstein series 128 0 128

Trace form

\( 1440q - 8q^{3} - 8q^{7} + O(q^{10}) \) \( 1440q - 8q^{3} - 8q^{7} + 8q^{10} + 8q^{12} - 16q^{13} - 8q^{15} + 360q^{16} + 8q^{22} + 192q^{25} + 16q^{27} + 32q^{28} - 24q^{30} - 32q^{33} + 80q^{34} + 32q^{37} + 16q^{40} - 24q^{42} + 32q^{43} + 8q^{48} + 16q^{52} + 40q^{55} - 40q^{58} - 32q^{60} - 216q^{63} - 80q^{67} - 280q^{69} - 136q^{70} - 136q^{73} + 32q^{75} - 160q^{78} - 160q^{79} + 80q^{81} - 192q^{82} + 80q^{85} + 8q^{88} - 96q^{90} + 16q^{93} + 96q^{97} + O(q^{100}) \)

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

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