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Properties

Label 1550.3.bg
Level $1550$
Weight $3$
Character orbit 1550.bg
Rep. character $\chi_{1550}(61,\cdot)$
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.bg (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

\( 640 q - 320 q^{4} - 48 q^{5} + 16 q^{7} + 520 q^{9} + O(q^{10}) \) \( 640 q - 320 q^{4} - 48 q^{5} + 16 q^{7} + 520 q^{9} - 16 q^{10} - 640 q^{16} + 24 q^{20} - 48 q^{25} - 48 q^{28} + 40 q^{33} - 12 q^{35} + 1040 q^{36} + 208 q^{38} - 32 q^{40} + 180 q^{41} - 532 q^{45} - 60 q^{47} + 4560 q^{49} + 96 q^{50} + 440 q^{51} + 60 q^{59} - 244 q^{62} - 136 q^{63} - 1280 q^{64} + 564 q^{67} + 440 q^{69} + 712 q^{70} + 280 q^{71} - 744 q^{78} + 48 q^{80} - 1180 q^{81} - 192 q^{82} - 900 q^{87} + 1008 q^{90} - 100 q^{93} + 1068 q^{95} + 432 q^{97} - 544 q^{98} + O(q^{100}) \)

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

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