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Properties

Label 1550.2.bn
Level $1550$
Weight $2$
Character orbit 1550.bn
Rep. character $\chi_{1550}(81,\cdot)$
Character field $\Q(\zeta_{15})$
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.bn (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 640 q + 8 q^{3} - 160 q^{4} - 2 q^{5} + 4 q^{6} + 16 q^{7} + 88 q^{9} + O(q^{10}) \) \( 640 q + 8 q^{3} - 160 q^{4} - 2 q^{5} + 4 q^{6} + 16 q^{7} + 88 q^{9} + 4 q^{10} + 4 q^{11} - 2 q^{12} - 160 q^{16} - 12 q^{20} - 32 q^{21} - 12 q^{22} + 24 q^{23} + 4 q^{24} - 48 q^{25} - 48 q^{26} + 20 q^{27} - 14 q^{28} + 112 q^{29} + 26 q^{30} + 16 q^{31} + 16 q^{33} + 8 q^{34} + 16 q^{35} + 78 q^{36} + 32 q^{37} + 4 q^{40} - 42 q^{41} + 34 q^{42} + 24 q^{43} - 16 q^{44} + 64 q^{45} - 20 q^{46} + 18 q^{47} - 12 q^{48} + 96 q^{49} + 72 q^{50} - 112 q^{51} + 12 q^{53} - 68 q^{54} - 28 q^{55} - 68 q^{57} + 32 q^{58} - 32 q^{59} - 20 q^{60} - 24 q^{61} + 12 q^{62} + 48 q^{63} - 160 q^{64} - 188 q^{65} - 108 q^{67} - 12 q^{69} - 28 q^{70} + 54 q^{71} - 68 q^{73} + 20 q^{74} + 72 q^{75} - 20 q^{77} + 52 q^{78} + 88 q^{79} - 2 q^{80} + 114 q^{81} + 12 q^{82} + 82 q^{83} + 8 q^{84} + 72 q^{85} + 68 q^{86} + 54 q^{87} - 12 q^{88} - 114 q^{89} + 128 q^{90} + 56 q^{91} - 6 q^{92} - 136 q^{93} - 30 q^{95} + 4 q^{96} + 30 q^{97} - 28 q^{98} - 160 q^{99} + O(q^{100}) \)

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

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