↑

Properties

Label 720.2.cm
Level $720$
Weight $2$
Character orbit 720.cm
Rep. character $\chi_{720}(77,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $560$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.cm (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 720 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(720, [\chi])\).

Total New Old
Modular forms 592 592 0
Cusp forms 560 560 0
Eisenstein series 32 32 0

Trace form

\( 560 q - 6 q^{2} - 8 q^{3} - 6 q^{5} - 8 q^{6} + O(q^{10}) \) \( 560 q - 6 q^{2} - 8 q^{3} - 6 q^{5} - 8 q^{6} - 16 q^{10} - 12 q^{11} + 2 q^{12} - 4 q^{13} - 8 q^{15} - 4 q^{16} - 36 q^{18} - 6 q^{20} - 8 q^{21} - 10 q^{22} + 24 q^{24} - 8 q^{27} + 8 q^{28} + 4 q^{30} - 8 q^{31} - 66 q^{32} - 8 q^{33} + 12 q^{34} + 8 q^{36} - 16 q^{37} + 6 q^{38} + 24 q^{39} - 12 q^{40} + 14 q^{42} - 14 q^{45} - 40 q^{46} - 12 q^{47} - 38 q^{48} - 6 q^{50} - 8 q^{51} + 14 q^{52} - 24 q^{54} - 12 q^{56} - 24 q^{57} + 6 q^{58} - 16 q^{60} - 4 q^{61} + 20 q^{63} + 24 q^{64} - 12 q^{65} + 24 q^{66} - 30 q^{68} - 12 q^{69} - 6 q^{70} + 18 q^{72} - 24 q^{74} - 54 q^{75} + 8 q^{76} + 30 q^{78} - 16 q^{81} - 12 q^{83} + 12 q^{84} + 8 q^{85} - 12 q^{86} - 12 q^{87} - 42 q^{88} - 46 q^{90} - 16 q^{91} - 120 q^{92} + 4 q^{93} - 12 q^{95} + 48 q^{96} - 4 q^{97} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(720, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
720.2.cm.a 720.cm 720.bm $560$ $5.749$ None \(-6\) \(-8\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{12}]$