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Properties

Label 1550.3.o
Level $1550$
Weight $3$
Character orbit 1550.o
Rep. character $\chi_{1550}(801,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $204$
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.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 984 204 780
Cusp forms 936 204 732
Eisenstein series 48 0 48

Trace form

\( 204 q - 6 q^{3} + 408 q^{4} + 10 q^{7} + 292 q^{9} + O(q^{10}) \) \( 204 q - 6 q^{3} + 408 q^{4} + 10 q^{7} + 292 q^{9} - 6 q^{11} - 12 q^{12} - 18 q^{13} + 4 q^{14} + 816 q^{16} - 30 q^{17} - 16 q^{18} - 34 q^{19} - 162 q^{21} + 36 q^{22} + 48 q^{26} + 20 q^{28} - 8 q^{31} + 308 q^{33} - 48 q^{34} + 584 q^{36} - 18 q^{37} - 112 q^{38} + 188 q^{39} - 130 q^{41} - 48 q^{42} + 138 q^{43} - 12 q^{44} + 16 q^{47} - 24 q^{48} - 760 q^{49} + 30 q^{51} - 36 q^{52} + 126 q^{53} + 8 q^{56} - 6 q^{57} + 46 q^{59} - 156 q^{62} - 168 q^{63} + 1632 q^{64} - 32 q^{66} - 18 q^{67} - 60 q^{68} - 192 q^{69} - 78 q^{71} - 32 q^{72} + 162 q^{73} + 192 q^{74} - 68 q^{76} + 496 q^{78} - 258 q^{79} - 1254 q^{81} - 112 q^{82} + 594 q^{83} - 324 q^{84} - 264 q^{86} - 64 q^{87} + 72 q^{88} - 250 q^{93} + 432 q^{94} + 512 q^{97} + 160 q^{98} + 132 q^{99} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(1550, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(775, [\chi])\)\(^{\oplus 2}\)