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Properties

Label 1550.2.ch
Level $1550$
Weight $2$
Character orbit 1550.ch
Rep. character $\chi_{1550}(59,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $640$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1550 = 2 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1550.ch (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1550, [\chi])\).

Total New Old
Modular forms 1952 640 1312
Cusp forms 1888 640 1248
Eisenstein series 64 0 64

Trace form

\( 640 q + 10 q^{3} - 640 q^{4} + 2 q^{5} - 4 q^{6} - 82 q^{9} + O(q^{10}) \) \( 640 q + 10 q^{3} - 640 q^{4} + 2 q^{5} - 4 q^{6} - 82 q^{9} + 4 q^{10} - 4 q^{11} - 10 q^{12} - 8 q^{15} + 640 q^{16} - 2 q^{20} - 8 q^{21} + 10 q^{22} + 20 q^{23} + 4 q^{24} - 22 q^{25} + 48 q^{26} + 40 q^{27} - 8 q^{29} - 28 q^{30} - 16 q^{31} - 30 q^{33} - 32 q^{34} + 2 q^{35} + 82 q^{36} - 10 q^{37} - 20 q^{38} - 4 q^{40} - 48 q^{41} + 10 q^{42} + 20 q^{43} + 4 q^{44} - 26 q^{45} - 50 q^{47} + 10 q^{48} - 84 q^{49} - 68 q^{51} + 20 q^{53} - 68 q^{54} + 28 q^{55} - 60 q^{57} + 8 q^{59} + 8 q^{60} + 24 q^{61} + 40 q^{62} - 40 q^{63} - 640 q^{64} - 54 q^{65} - 30 q^{67} + 188 q^{69} + 24 q^{70} - 34 q^{71} - 40 q^{73} + 20 q^{74} + 42 q^{75} + 130 q^{77} + 40 q^{78} - 32 q^{79} + 2 q^{80} + 76 q^{81} + 180 q^{83} + 8 q^{84} - 16 q^{85} - 68 q^{86} - 60 q^{87} - 10 q^{88} - 94 q^{89} - 20 q^{90} - 26 q^{91} - 20 q^{92} + 80 q^{93} + 88 q^{95} - 4 q^{96} + 20 q^{98} - 10 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1550, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1550, [\chi])\) into lower level spaces

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