Properties

Label 560.5.cy
Level $560$
Weight $5$
Character orbit 560.cy
Rep. character $\chi_{560}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1520$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 560.cy (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 560 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(560, [\chi])\).

Total New Old
Modular forms 1552 1552 0
Cusp forms 1520 1520 0
Eisenstein series 32 32 0

Trace form

\( 1520 q - 2 q^{2} - 2 q^{5} - 16 q^{6} - 188 q^{8} + 20088 q^{9} + O(q^{10}) \) \( 1520 q - 2 q^{2} - 2 q^{5} - 16 q^{6} - 188 q^{8} + 20088 q^{9} - 66 q^{10} - 4 q^{11} - 326 q^{12} - 16 q^{15} - 4 q^{16} - 4 q^{17} + 224 q^{18} + 1504 q^{20} - 8 q^{21} - 72 q^{22} + 324 q^{24} - 4 q^{26} - 2602 q^{28} - 3954 q^{30} - 8 q^{31} - 3302 q^{32} - 4 q^{33} + 1872 q^{34} + 1338 q^{35} + 2032 q^{36} - 2908 q^{38} + 648 q^{39} - 2832 q^{40} + 9486 q^{42} - 16 q^{43} - 2088 q^{44} + 2660 q^{45} - 4 q^{46} - 4 q^{47} + 3988 q^{48} - 8 q^{50} - 4 q^{51} - 20020 q^{52} - 4 q^{53} - 584 q^{54} - 8 q^{56} - 648 q^{57} - 1914 q^{58} - 6528 q^{59} - 2048 q^{60} - 4 q^{61} + 37856 q^{62} + 9596 q^{63} - 4 q^{65} - 8860 q^{66} - 2884 q^{67} + 1944 q^{68} - 648 q^{69} - 19464 q^{70} - 27168 q^{72} - 17012 q^{74} - 326 q^{75} - 16 q^{76} - 9612 q^{77} - 10520 q^{78} - 17216 q^{80} - 507392 q^{81} + 47030 q^{82} + 6444 q^{84} - 2508 q^{85} + 15908 q^{86} + 324 q^{87} - 3904 q^{88} - 121276 q^{90} + 7288 q^{91} - 6004 q^{92} + 17688 q^{94} + 25340 q^{95} + 72068 q^{96} - 16 q^{97} + 29034 q^{98} - 648 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

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