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Properties

Label 2850.2.bk
Level $2850$
Weight $2$
Character orbit 2850.bk
Rep. character $\chi_{2850}(401,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $756$
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.bk (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
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 756 2988
Cusp forms 3456 756 2700
Eisenstein series 288 0 288

Trace form

\( 756 q + 3 q^{3} + 3 q^{6} - 3 q^{9} + O(q^{10}) \) \( 756 q + 3 q^{3} + 3 q^{6} - 3 q^{9} - 24 q^{13} - 36 q^{19} - 24 q^{22} + 3 q^{24} - 9 q^{27} + 12 q^{28} + 21 q^{33} - 12 q^{34} - 3 q^{36} - 84 q^{39} - 36 q^{43} - 36 q^{46} + 6 q^{48} - 414 q^{49} - 81 q^{51} - 12 q^{52} + 18 q^{54} + 132 q^{57} + 24 q^{58} + 24 q^{61} + 30 q^{63} - 378 q^{64} - 63 q^{66} + 18 q^{67} + 54 q^{69} + 6 q^{72} - 84 q^{73} + 6 q^{78} - 36 q^{79} - 51 q^{81} + 6 q^{82} + 54 q^{84} + 42 q^{87} + 72 q^{91} + 150 q^{93} + 66 q^{97} + 192 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1425, [\chi])\)\(^{\oplus 2}\)