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Properties

Label 720.2.cp
Level $720$
Weight $2$
Character orbit 720.cp
Rep. character $\chi_{720}(43,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $560$
Newform subspaces $3$
Sturm bound $288$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.cp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 720 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 3 \)
Sturm bound: \(288\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\)

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

\( 560 q - 2 q^{2} - 2 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + O(q^{10}) \) \( 560 q - 2 q^{2} - 2 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{11} - 10 q^{12} - 4 q^{13} - 12 q^{15} - 4 q^{16} - 16 q^{17} + 28 q^{18} - 2 q^{20} - 8 q^{21} - 10 q^{22} - 4 q^{23} + 24 q^{24} + 16 q^{26} - 24 q^{28} - 12 q^{30} - 22 q^{32} - 8 q^{33} + 12 q^{34} + 12 q^{35} + 8 q^{36} - 16 q^{37} - 34 q^{38} + 8 q^{40} + 46 q^{42} - 4 q^{43} + 64 q^{44} + 6 q^{45} + 8 q^{46} - 50 q^{48} - 2 q^{50} - 8 q^{51} + 14 q^{52} + 8 q^{54} - 16 q^{55} - 4 q^{56} + 24 q^{57} - 10 q^{58} - 84 q^{60} - 4 q^{61} - 76 q^{62} - 24 q^{64} - 4 q^{65} - 40 q^{66} - 4 q^{67} - 46 q^{68} - 12 q^{69} - 6 q^{70} - 32 q^{71} + 14 q^{72} - 64 q^{74} + 46 q^{75} - 16 q^{76} + 2 q^{78} - 204 q^{80} - 16 q^{81} - 16 q^{82} + 60 q^{84} - 12 q^{85} - 4 q^{86} - 64 q^{87} + 6 q^{88} - 14 q^{90} - 16 q^{91} + 20 q^{92} - 20 q^{93} - 64 q^{96} - 4 q^{97} + 108 q^{98} + 32 q^{99} + O(q^{100}) \)

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.cp.a 720.cp 720.bp $4$ $5.749$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2\zeta_{12}+\cdots)q^{3}+\cdots\)
720.2.cp.b 720.cp 720.bp $4$ $5.749$ \(\Q(\zeta_{12})\) None \(4\) \(0\) \(4\) \(6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12}^{3})q^{2}+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
720.2.cp.c 720.cp 720.bp $552$ $5.749$ None \(-4\) \(0\) \(-4\) \(-10\) $\mathrm{SU}(2)[C_{12}]$