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Properties

Label 2850.2.by
Level $2850$
Weight $2$
Character orbit 2850.by
Rep. character $\chi_{2850}(221,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1600$
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.by (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

\( 1600 q + 200 q^{4} + O(q^{10}) \) \( 1600 q + 200 q^{4} - 66 q^{15} + 200 q^{16} - 12 q^{19} + 36 q^{22} - 20 q^{25} - 4 q^{30} + 36 q^{33} + 24 q^{39} - 32 q^{42} + 40 q^{43} - 164 q^{45} + 1664 q^{49} - 60 q^{51} + 12 q^{54} + 4 q^{55} + 84 q^{57} + 6 q^{60} + 24 q^{61} + 36 q^{63} - 400 q^{64} - 16 q^{66} + 24 q^{67} + 12 q^{70} - 80 q^{73} + 8 q^{76} + 24 q^{78} + 8 q^{81} + 112 q^{85} + 272 q^{87} + 54 q^{90} - 4 q^{93} - 48 q^{97} + 32 q^{99} + O(q^{100}) \)

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

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