Properties

Label 2850.2.ci
Level $2850$
Weight $2$
Character orbit 2850.ci
Rep. character $\chi_{2850}(83,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3200$
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.ci (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1425 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 9728 3200 6528
Cusp forms 9472 3200 6272
Eisenstein series 256 0 256

Trace form

\( 3200q + O(q^{10}) \) \( 3200q + 16q^{13} - 12q^{15} - 400q^{16} - 32q^{18} + 40q^{19} - 32q^{22} - 8q^{25} - 24q^{27} - 12q^{33} + 16q^{37} + 80q^{39} + 32q^{42} + 40q^{43} + 216q^{45} - 16q^{52} + 8q^{55} - 68q^{57} + 8q^{60} + 52q^{63} - 136q^{67} + 8q^{70} - 16q^{72} - 64q^{73} - 296q^{75} - 16q^{78} + 240q^{84} + 48q^{85} + 32q^{87} - 16q^{88} + 4q^{90} + 20q^{93} + 16q^{97} + O(q^{100}) \)

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

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