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Properties

Label 720.2.ce
Level $720$
Weight $2$
Character orbit 720.ce
Rep. character $\chi_{720}(229,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $560$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.ce (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

\( 560 q - 4 q^{4} - 2 q^{5} - 8 q^{6} + O(q^{10}) \) \( 560 q - 4 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{10} - 4 q^{11} + 12 q^{14} - 8 q^{15} - 4 q^{16} - 16 q^{19} - 16 q^{20} + 4 q^{21} + 8 q^{24} - 48 q^{26} - 4 q^{29} + 26 q^{30} - 8 q^{31} + 4 q^{34} + 12 q^{35} - 64 q^{36} - 2 q^{40} - 16 q^{44} - 14 q^{45} + 24 q^{46} - 240 q^{49} + 32 q^{50} + 16 q^{51} - 64 q^{54} - 32 q^{56} - 4 q^{59} + 30 q^{60} - 4 q^{61} - 16 q^{64} - 4 q^{65} - 168 q^{66} + 4 q^{69} - 16 q^{70} - 4 q^{74} + 58 q^{75} + 8 q^{76} - 8 q^{79} + 112 q^{80} - 16 q^{81} - 160 q^{84} + 8 q^{85} - 44 q^{86} + 88 q^{90} + 40 q^{91} - 20 q^{94} - 4 q^{95} + 80 q^{96} - 76 q^{99} + O(q^{100}) \)

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.ce.a 720.ce 720.be $560$ $5.749$ None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{12}]$