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Properties

Label 2850.2.cr
Level $2850$
Weight $2$
Character orbit 2850.cr
Rep. character $\chi_{2850}(17,\cdot)$
Character field $\Q(\zeta_{180})$
Dimension $9600$
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.cr (of order \(180\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1425 \)
Character field: \(\Q(\zeta_{180})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 29184 9600 19584
Cusp forms 28416 9600 18816
Eisenstein series 768 0 768

Trace form

\( 9600 q + O(q^{10}) \) \( 9600 q + 36 q^{15} + 48 q^{18} + 96 q^{22} + 24 q^{25} - 72 q^{33} - 24 q^{43} + 36 q^{45} + 120 q^{55} + 132 q^{57} + 48 q^{60} + 36 q^{63} - 48 q^{67} + 48 q^{70} + 48 q^{78} + 180 q^{84} - 192 q^{85} + 96 q^{87} + 168 q^{90} + 228 q^{93} - 48 q^{97} + O(q^{100}) \)

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

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