Properties

Label 2850.2.cb
Level $2850$
Weight $2$
Character orbit 2850.cb
Rep. character $\chi_{2850}(193,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $720$
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.cb (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
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 720 6768
Cusp forms 6912 720 6192
Eisenstein series 576 0 576

Trace form

\( 720q - 24q^{7} + O(q^{10}) \) \( 720q - 24q^{7} + 48q^{21} + 24q^{22} + 48q^{23} - 48q^{26} - 24q^{33} - 48q^{41} - 120q^{43} - 48q^{47} + 72q^{53} - 24q^{57} - 24q^{61} - 48q^{62} - 144q^{67} - 24q^{68} - 72q^{73} + 48q^{76} + 48q^{78} + 96q^{82} + 48q^{83} + 192q^{86} - 24q^{87} + 264q^{91} + 96q^{92} + 192q^{97} + 192q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1425, [\chi])\)\(^{\oplus 2}\)