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Properties

Label 2850.2.bl
Level $2850$
Weight $2$
Character orbit 2850.bl
Rep. character $\chi_{2850}(199,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $360$
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.bl (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
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 360 3384
Cusp forms 3456 360 3096
Eisenstein series 288 0 288

Trace form

\( 360 q + O(q^{10}) \) \( 360 q + 24 q^{11} - 48 q^{14} + 24 q^{19} - 24 q^{21} + 24 q^{26} - 48 q^{29} - 24 q^{41} + 24 q^{44} + 24 q^{46} + 156 q^{49} - 48 q^{59} - 84 q^{61} + 180 q^{64} - 48 q^{69} + 144 q^{71} + 72 q^{74} - 24 q^{76} + 168 q^{79} - 24 q^{84} + 96 q^{86} + 96 q^{89} + 156 q^{91} + 240 q^{94} + 24 q^{99} + O(q^{100}) \)

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

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