Properties

Label 2850.2.cc
Level $2850$
Weight $2$
Character orbit 2850.cc
Rep. character $\chi_{2850}(443,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1440$
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.cc (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 285 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 7488 1440 6048
Cusp forms 6912 1440 5472
Eisenstein series 576 0 576

Trace form

\( 1440q + O(q^{10}) \) \( 1440q + 48q^{18} - 24q^{22} - 72q^{33} - 24q^{43} + 132q^{51} - 108q^{57} - 24q^{61} + 36q^{63} - 132q^{66} - 48q^{67} + 48q^{78} + 288q^{81} + 96q^{87} + 168q^{91} + 228q^{93} - 48q^{97} + O(q^{100}) \)

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

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