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Properties

Label 720.2.da
Level $720$
Weight $2$
Character orbit 720.da
Rep. character $\chi_{720}(59,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $560$
Newform subspaces $5$
Sturm bound $288$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.da (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 720 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
Sturm bound: \(288\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\), \(11\)

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

\( 560 q - 4 q^{4} - 6 q^{5} - 8 q^{6} + O(q^{10}) \) \( 560 q - 4 q^{4} - 6 q^{5} - 8 q^{6} - 8 q^{10} - 12 q^{11} - 12 q^{14} - 4 q^{16} - 16 q^{19} + 36 q^{20} - 20 q^{21} + 8 q^{24} - 12 q^{29} - 14 q^{30} - 12 q^{34} + 16 q^{36} - 16 q^{39} - 2 q^{40} + 6 q^{45} - 24 q^{46} + 224 q^{49} - 84 q^{50} - 32 q^{51} + 48 q^{54} - 16 q^{55} - 96 q^{56} - 12 q^{59} + 14 q^{60} - 4 q^{61} - 16 q^{64} - 12 q^{65} - 88 q^{66} + 4 q^{69} + 12 q^{70} - 12 q^{74} - 54 q^{75} - 16 q^{76} - 16 q^{81} + 88 q^{84} - 12 q^{85} - 132 q^{86} - 24 q^{90} - 72 q^{91} - 20 q^{94} - 96 q^{96} - 4 q^{99} + O(q^{100}) \)

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.da.a 720.da 720.ca $4$ $5.749$ \(\Q(\zeta_{12})\) None \(-2\) \(-6\) \(-2\) \(-12\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
720.2.da.b 720.da 720.ca $4$ $5.749$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(4\) \(-12\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}+\cdots\)
720.2.da.c 720.da 720.ca $4$ $5.749$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(2\) \(12\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\)
720.2.da.d 720.da 720.ca $4$ $5.749$ \(\Q(\zeta_{12})\) None \(2\) \(6\) \(-4\) \(12\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
720.2.da.e 720.da 720.ca $544$ $5.749$ None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{12}]$