↑

Properties

Label 1850.2.s
Level $1850$
Weight $2$
Character orbit 1850.s
Rep. character $\chi_{1850}(519,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $360$
Sturm bound $570$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1850.s (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(570\)

Dimensions

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

Total New Old
Modular forms 1160 360 800
Cusp forms 1128 360 768
Eisenstein series 32 0 32

Trace form

\( 360 q + 90 q^{4} + 4 q^{5} - 4 q^{6} + 90 q^{9} + O(q^{10}) \) \( 360 q + 90 q^{4} + 4 q^{5} - 4 q^{6} + 90 q^{9} + 4 q^{10} + 12 q^{11} + 8 q^{14} + 40 q^{15} - 90 q^{16} - 20 q^{17} - 20 q^{19} - 4 q^{20} - 24 q^{21} - 20 q^{23} - 16 q^{24} + 24 q^{25} + 60 q^{27} - 20 q^{28} - 12 q^{29} - 20 q^{30} + 12 q^{31} + 60 q^{33} - 36 q^{35} - 90 q^{36} + 16 q^{39} - 4 q^{40} + 20 q^{42} + 8 q^{44} + 40 q^{45} + 100 q^{47} - 312 q^{49} - 8 q^{50} - 8 q^{51} + 40 q^{53} + 40 q^{54} - 36 q^{55} - 8 q^{56} + 12 q^{59} + 20 q^{60} - 20 q^{61} + 60 q^{62} - 40 q^{63} + 90 q^{64} - 100 q^{65} - 16 q^{66} - 52 q^{69} + 20 q^{71} - 40 q^{74} + 90 q^{75} + 40 q^{77} + 10 q^{78} + 4 q^{80} - 66 q^{81} - 100 q^{83} - 36 q^{84} + 64 q^{85} - 24 q^{86} - 140 q^{87} + 20 q^{88} - 12 q^{89} + 70 q^{90} + 32 q^{91} + 40 q^{92} + 48 q^{94} - 36 q^{95} - 4 q^{96} - 20 q^{97} + 80 q^{98} + 60 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(925, [\chi])\)\(^{\oplus 2}\)