↑

Properties

Label 1550.3.t
Level $1550$
Weight $3$
Character orbit 1550.t
Rep. character $\chi_{1550}(89,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $640$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1550 = 2 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1550.t (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1550, [\chi])\).

Total New Old
Modular forms 1936 640 1296
Cusp forms 1904 640 1264
Eisenstein series 32 0 32

Trace form

\( 640 q + 320 q^{4} - 12 q^{5} + 20 q^{7} - 440 q^{9} + O(q^{10}) \) \( 640 q + 320 q^{4} - 12 q^{5} + 20 q^{7} - 440 q^{9} - 16 q^{10} + 20 q^{12} - 640 q^{16} - 36 q^{20} + 108 q^{25} - 90 q^{27} + 40 q^{28} - 60 q^{30} + 100 q^{31} + 64 q^{35} + 980 q^{36} + 250 q^{37} + 32 q^{40} - 30 q^{41} - 120 q^{42} + 180 q^{43} + 146 q^{45} - 200 q^{46} - 110 q^{47} + 80 q^{48} + 1100 q^{49} + 48 q^{50} + 110 q^{51} - 160 q^{53} - 720 q^{55} - 700 q^{57} + 160 q^{59} - 60 q^{60} - 160 q^{62} - 240 q^{63} + 1280 q^{64} + 360 q^{65} - 40 q^{69} + 96 q^{70} + 180 q^{71} + 40 q^{73} - 70 q^{75} - 280 q^{77} + 420 q^{78} - 100 q^{79} - 48 q^{80} - 1810 q^{81} + 480 q^{82} - 930 q^{83} - 180 q^{85} - 300 q^{86} + 730 q^{87} - 150 q^{89} - 392 q^{90} - 220 q^{92} - 430 q^{93} + 94 q^{95} - 890 q^{97} + 320 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1550, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1550, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1550, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(775, [\chi])\)\(^{\oplus 2}\)