↑

Properties

Label 2850.2.bw
Level $2850$
Weight $2$
Character orbit 2850.bw
Rep. character $\chi_{2850}(179,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1600$
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.bw (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1425 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 4864 1600 3264
Cusp forms 4736 1600 3136
Eisenstein series 128 0 128

Trace form

\( 1600 q - 200 q^{4} + O(q^{10}) \) \( 1600 q - 200 q^{4} + 30 q^{15} + 200 q^{16} - 12 q^{19} + 60 q^{22} + 12 q^{25} + 4 q^{30} + 24 q^{39} + 28 q^{45} - 1536 q^{49} + 60 q^{51} + 12 q^{54} - 12 q^{55} - 30 q^{60} - 24 q^{61} + 40 q^{63} + 400 q^{64} + 16 q^{66} - 36 q^{70} + 80 q^{73} - 8 q^{76} - 8 q^{81} - 32 q^{85} + 54 q^{90} + 32 q^{99} + O(q^{100}) \)

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

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