Properties

Label 2850.2.bo
Level $2850$
Weight $2$
Character orbit 2850.bo
Rep. character $\chi_{2850}(299,\cdot)$
Character field $\Q(\zeta_{18})$
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.bo (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 285 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 3744 720 3024
Cusp forms 3456 720 2736
Eisenstein series 288 0 288

Trace form

\( 720q + O(q^{10}) \) \( 720q + 24q^{19} + 96q^{39} + 72q^{46} + 264q^{49} + 150q^{51} - 36q^{54} + 108q^{61} + 360q^{64} + 126q^{66} + 24q^{79} + 144q^{81} + 108q^{84} + 108q^{91} + 60q^{99} + O(q^{100}) \)

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

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