Properties

Label 1850.2.h
Level $1850$
Weight $2$
Character orbit 1850.h
Rep. character $\chi_{1850}(857,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $114$
Sturm bound $570$

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Defining parameters

Level: \( N \) \(=\) \( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1850.h (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(i)\)
Sturm bound: \(570\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1850, [\chi])\).

Total New Old
Modular forms 594 114 480
Cusp forms 546 114 432
Eisenstein series 48 0 48

Trace form

\( 114 q + 2 q^{2} - 8 q^{3} + 114 q^{4} + 2 q^{8} + O(q^{10}) \) \( 114 q + 2 q^{2} - 8 q^{3} + 114 q^{4} + 2 q^{8} - 8 q^{12} + 8 q^{13} - 8 q^{14} + 114 q^{16} + 16 q^{19} + 8 q^{23} + 16 q^{26} + 40 q^{27} - 6 q^{29} - 8 q^{31} + 2 q^{32} + 38 q^{37} + 56 q^{39} - 16 q^{43} + 8 q^{47} - 8 q^{48} + 8 q^{52} + 6 q^{53} - 8 q^{56} - 48 q^{57} + 18 q^{58} + 40 q^{59} - 34 q^{61} + 40 q^{62} + 114 q^{64} + 16 q^{66} - 16 q^{67} + 56 q^{69} + 32 q^{71} - 2 q^{73} - 22 q^{74} + 16 q^{76} + 40 q^{77} + 20 q^{78} + 24 q^{79} + 30 q^{81} - 20 q^{83} + 32 q^{86} - 58 q^{89} + 8 q^{92} + 48 q^{93} - 72 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1850, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(925, [\chi])\)\(^{\oplus 2}\)