Properties

Label 2850.2.cm
Level $2850$
Weight $2$
Character orbit 2850.cm
Rep. character $\chi_{2850}(29,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $4800$
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.cm (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1425 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 14592 4800 9792
Cusp forms 14208 4800 9408
Eisenstein series 384 0 384

Trace form

\( 4800q + O(q^{10}) \) \( 4800q - 30q^{15} - 60q^{22} + 108q^{25} + 54q^{45} - 108q^{46} + 2304q^{49} + 120q^{51} - 36q^{54} - 60q^{55} - 6q^{60} - 144q^{61} - 600q^{64} + 96q^{66} + 96q^{81} - 162q^{84} - 72q^{85} + 36q^{90} + 192q^{99} + O(q^{100}) \)

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

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