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Properties

Label 560.5.cg
Level $560$
Weight $5$
Character orbit 560.cg
Rep. character $\chi_{560}(53,\cdot)$
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.cg (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

\( 1520 q - 2 q^{2} - 4 q^{3} - 2 q^{5} - 16 q^{6} - 188 q^{8} - 20088 q^{9} + O(q^{10}) \) \( 1520 q - 2 q^{2} - 4 q^{3} - 2 q^{5} - 16 q^{6} - 188 q^{8} - 20088 q^{9} + 62 q^{10} - 4 q^{11} + 322 q^{12} - 16 q^{13} - 16 q^{15} - 4 q^{16} - 4 q^{17} - 100 q^{18} - 1520 q^{20} - 8 q^{21} + 56 q^{22} - 324 q^{24} - 4 q^{26} + 632 q^{27} + 3618 q^{28} + 1590 q^{30} - 8 q^{31} + 3298 q^{32} - 4 q^{33} - 1872 q^{34} + 3838 q^{35} + 2032 q^{36} - 4 q^{37} + 2904 q^{38} - 648 q^{39} - 332 q^{40} + 9874 q^{42} + 2088 q^{44} + 2336 q^{45} - 4 q^{46} - 4 q^{47} + 4636 q^{48} - 8 q^{50} - 4 q^{51} + 9756 q^{52} + 584 q^{54} - 8 q^{56} + 648 q^{57} + 3670 q^{58} + 6528 q^{59} + 2628 q^{60} - 4 q^{61} + 37856 q^{62} + 9596 q^{63} - 4 q^{65} - 8860 q^{66} - 3996 q^{68} + 648 q^{69} + 21892 q^{70} + 10780 q^{72} + 17012 q^{74} + 322 q^{75} - 16 q^{76} - 30608 q^{78} + 17212 q^{80} - 507392 q^{81} - 49570 q^{82} - 16 q^{83} - 6444 q^{84} + 2492 q^{85} + 15908 q^{86} - 324 q^{87} + 41520 q^{88} + 153012 q^{90} + 7288 q^{91} - 6004 q^{92} + 644 q^{93} - 17688 q^{94} + 25340 q^{95} + 72068 q^{96} - 16 q^{97} - 27786 q^{98} + 648 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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