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Properties

Label 1550.3.z
Level $1550$
Weight $3$
Character orbit 1550.z
Rep. character $\chi_{1550}(461,\cdot)$
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.z (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

\( 640 q - 320 q^{4} + 12 q^{5} - 4 q^{7} + 520 q^{9} + O(q^{10}) \) \( 640 q - 320 q^{4} + 12 q^{5} - 4 q^{7} + 520 q^{9} - 16 q^{10} + 20 q^{12} - 640 q^{16} - 36 q^{20} + 12 q^{25} - 90 q^{27} - 8 q^{28} - 180 q^{30} - 100 q^{31} + 40 q^{33} - 232 q^{35} + 940 q^{36} + 70 q^{37} + 48 q^{38} - 32 q^{40} + 30 q^{41} + 120 q^{42} + 180 q^{43} + 218 q^{45} + 200 q^{46} + 50 q^{47} - 1140 q^{49} - 144 q^{50} - 110 q^{51} + 160 q^{53} - 720 q^{55} + 160 q^{59} - 220 q^{60} + 216 q^{62} + 104 q^{63} - 1280 q^{64} + 880 q^{65} - 456 q^{67} - 60 q^{69} - 448 q^{70} + 180 q^{71} + 320 q^{73} + 70 q^{75} + 280 q^{77} + 76 q^{78} - 100 q^{79} + 48 q^{80} - 1630 q^{81} + 288 q^{82} - 930 q^{83} + 300 q^{85} + 300 q^{86} - 330 q^{87} - 150 q^{89} + 168 q^{90} + 220 q^{92} - 630 q^{93} - 622 q^{95} - 498 q^{97} - 224 q^{98} + O(q^{100}) \)

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

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