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Properties

Label 1550.3.cn
Level $1550$
Weight $3$
Character orbit 1550.cn
Rep. character $\chi_{1550}(179,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1280$
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.cn (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 3872 1280 2592
Cusp forms 3808 1280 2528
Eisenstein series 64 0 64

Trace form

\( 1280 q - 10 q^{3} - 2560 q^{4} - 6 q^{5} + 490 q^{9} + O(q^{10}) \) \( 1280 q - 10 q^{3} - 2560 q^{4} - 6 q^{5} + 490 q^{9} + 16 q^{10} + 20 q^{12} - 110 q^{15} + 5120 q^{16} + 12 q^{20} + 80 q^{22} - 20 q^{23} + 22 q^{25} - 340 q^{27} - 100 q^{31} + 280 q^{33} - 42 q^{35} - 980 q^{36} - 250 q^{37} + 80 q^{38} - 32 q^{40} - 240 q^{41} - 960 q^{42} - 180 q^{43} - 402 q^{45} + 170 q^{47} - 40 q^{48} - 1080 q^{49} - 16 q^{50} + 280 q^{51} + 220 q^{53} + 98 q^{55} + 240 q^{57} + 180 q^{59} + 220 q^{60} + 320 q^{62} - 240 q^{63} - 10240 q^{64} - 76 q^{65} - 390 q^{67} + 430 q^{69} + 8 q^{70} - 70 q^{71} - 40 q^{73} - 842 q^{75} + 40 q^{77} + 440 q^{78} + 400 q^{79} - 24 q^{80} + 1460 q^{81} - 1090 q^{83} - 120 q^{85} - 240 q^{86} + 180 q^{87} - 160 q^{88} + 150 q^{89} - 368 q^{90} - 450 q^{91} + 40 q^{92} + 120 q^{93} - 388 q^{95} + 320 q^{98} - 180 q^{99} + O(q^{100}) \)

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

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