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Properties

Label 780.2.cy
Level $780$
Weight $2$
Character orbit 780.cy
Rep. character $\chi_{780}(167,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $640$
Newform subspaces $1$
Sturm bound $336$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 780.cy (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 780 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(336\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(780, [\chi])\).

Total New Old
Modular forms 704 704 0
Cusp forms 640 640 0
Eisenstein series 64 64 0

Trace form

\( 640 q - 8 q^{6} + O(q^{10}) \) \( 640 q - 8 q^{6} - 20 q^{10} - 16 q^{13} - 8 q^{16} - 16 q^{21} - 12 q^{22} + 40 q^{24} - 36 q^{28} - 14 q^{30} - 12 q^{33} + 16 q^{34} - 12 q^{36} + 8 q^{37} + 8 q^{40} + 16 q^{42} + 12 q^{45} - 16 q^{46} - 92 q^{48} + 224 q^{49} - 12 q^{52} + 8 q^{54} + 36 q^{58} - 64 q^{60} - 16 q^{61} - 16 q^{66} - 16 q^{70} - 18 q^{72} - 48 q^{76} - 92 q^{78} - 8 q^{81} - 4 q^{82} - 112 q^{84} - 112 q^{85} - 108 q^{88} + 48 q^{90} + 8 q^{93} - 48 q^{94} - 64 q^{96} - 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(780, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
780.2.cy.a 780.cy 780.by $640$ $6.228$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$