↑

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 $1200$

Related objects

Downloads

Learn more

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

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

Display 100 coefficients 10 coefficients

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

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