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Properties

Label 1850.2.m
Level $1850$
Weight $2$
Character orbit 1850.m
Rep. character $\chi_{1850}(101,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $124$
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.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(570\)

Dimensions

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

Total New Old
Modular forms 596 124 472
Cusp forms 548 124 424
Eisenstein series 48 0 48

Trace form

\( 124 q + 62 q^{4} - 4 q^{7} - 70 q^{9} + O(q^{10}) \) \( 124 q + 62 q^{4} - 4 q^{7} - 70 q^{9} - 12 q^{13} - 62 q^{16} - 12 q^{19} - 16 q^{26} + 4 q^{28} + 16 q^{33} + 6 q^{34} - 140 q^{36} + 32 q^{37} - 16 q^{38} + 60 q^{39} + 2 q^{41} - 48 q^{42} - 16 q^{46} - 8 q^{47} - 58 q^{49} - 12 q^{52} + 8 q^{53} + 36 q^{57} - 8 q^{58} + 12 q^{59} - 30 q^{61} + 8 q^{62} + 8 q^{63} - 124 q^{64} - 36 q^{67} - 108 q^{69} - 8 q^{71} + 16 q^{73} - 8 q^{74} - 12 q^{76} + 40 q^{77} + 4 q^{78} - 48 q^{79} - 86 q^{81} + 28 q^{83} + 4 q^{86} + 84 q^{87} + 150 q^{89} + 120 q^{91} - 12 q^{92} - 36 q^{93} - 48 q^{94} + 24 q^{98} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(1850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(925, [\chi])\)\(^{\oplus 2}\)