Properties

Label 2850.2.c
Level $2850$
Weight $2$
Character orbit 2850.c
Rep. character $\chi_{2850}(2849,\cdot)$
Character field $\Q$
Dimension $120$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 285 \)
Character field: \(\Q\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 624 120 504
Cusp forms 576 120 456
Eisenstein series 48 0 48

Trace form

\( 120q - 120q^{4} + O(q^{10}) \) \( 120q - 120q^{4} + 120q^{16} - 4q^{19} - 16q^{39} - 96q^{49} + 36q^{54} + 24q^{61} - 120q^{64} + 12q^{66} + 4q^{76} + 16q^{81} + 116q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1425, [\chi])\)\(^{\oplus 2}\)