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Properties

Label 1550.3.w
Level $1550$
Weight $3$
Character orbit 1550.w
Rep. character $\chi_{1550}(339,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $640$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1550 = 2 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1550.w (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

\( 640 q + 10 q^{3} - 1280 q^{4} - 12 q^{5} - 490 q^{9} + O(q^{10}) \) \( 640 q + 10 q^{3} - 1280 q^{4} - 12 q^{5} - 490 q^{9} - 16 q^{10} - 20 q^{12} + 110 q^{15} + 2560 q^{16} + 24 q^{20} - 80 q^{22} + 20 q^{23} - 52 q^{25} - 170 q^{27} + 100 q^{31} + 50 q^{33} - 126 q^{35} + 980 q^{36} + 250 q^{37} - 80 q^{38} + 32 q^{40} - 30 q^{41} - 120 q^{42} + 180 q^{43} + 126 q^{45} - 170 q^{47} + 40 q^{48} + 1200 q^{49} - 32 q^{50} - 190 q^{51} - 220 q^{53} + 130 q^{55} + 480 q^{57} + 360 q^{59} - 220 q^{60} + 160 q^{62} + 240 q^{63} - 5120 q^{64} + 130 q^{65} + 390 q^{67} - 40 q^{69} + 316 q^{70} - 20 q^{71} + 40 q^{73} - 100 q^{75} - 40 q^{77} + 820 q^{78} + 200 q^{79} - 48 q^{80} - 1460 q^{81} - 50 q^{83} - 300 q^{86} - 180 q^{87} + 160 q^{88} - 150 q^{89} - 112 q^{90} + 450 q^{91} - 40 q^{92} + 600 q^{93} - 116 q^{95} - 320 q^{98} + O(q^{100}) \)

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

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