Properties

Label 770.2.bu
Level $770$
Weight $2$
Character orbit 770.bu
Rep. character $\chi_{770}(107,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $768$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.bu (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{60})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(770, [\chi])\).

Total New Old
Modular forms 2432 768 1664
Cusp forms 2176 768 1408
Eisenstein series 256 0 256

Trace form

\( 768 q - 8 q^{5} + 20 q^{7} + O(q^{10}) \) \( 768 q - 8 q^{5} + 20 q^{7} - 4 q^{11} + 24 q^{15} - 96 q^{16} + 40 q^{17} - 24 q^{22} + 8 q^{23} + 16 q^{25} + 8 q^{26} + 20 q^{28} - 84 q^{33} + 160 q^{36} + 40 q^{37} + 40 q^{41} + 20 q^{42} - 32 q^{45} - 80 q^{47} + 120 q^{51} - 40 q^{53} - 8 q^{55} - 16 q^{56} + 160 q^{57} + 48 q^{58} - 160 q^{61} - 100 q^{63} - 32 q^{67} - 40 q^{68} - 68 q^{70} - 32 q^{71} + 40 q^{73} - 112 q^{75} + 152 q^{77} - 12 q^{80} - 24 q^{81} - 16 q^{82} - 160 q^{85} + 12 q^{88} - 320 q^{90} + 92 q^{91} + 16 q^{92} - 40 q^{93} - 20 q^{95} - 56 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(770, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
770.2.bu.a 770.bu 385.av $768$ $6.148$ None \(0\) \(0\) \(-8\) \(20\) $\mathrm{SU}(2)[C_{60}]$

Decomposition of \(S_{2}^{\mathrm{old}}(770, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(770, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)