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Properties

Label 770.2.bh
Level $770$
Weight $2$
Character orbit 770.bh
Rep. character $\chi_{770}(57,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $288$
Newform subspaces $2$
Sturm bound $288$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.bh (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 1216 288 928
Cusp forms 1088 288 800
Eisenstein series 128 0 128

Trace form

\( 288 q + 8 q^{3} + O(q^{10}) \) \( 288 q + 8 q^{3} - 8 q^{11} + 32 q^{12} + 8 q^{15} + 72 q^{16} + 8 q^{20} + 8 q^{22} + 32 q^{23} - 16 q^{27} - 32 q^{31} + 40 q^{33} + 88 q^{36} - 8 q^{37} + 72 q^{38} - 96 q^{45} - 80 q^{46} - 24 q^{47} - 8 q^{48} - 80 q^{50} + 40 q^{51} - 80 q^{52} - 80 q^{53} - 160 q^{55} - 160 q^{57} - 40 q^{60} - 80 q^{62} - 48 q^{66} - 160 q^{67} + 16 q^{70} + 96 q^{71} - 72 q^{75} + 16 q^{77} - 32 q^{78} + 160 q^{81} - 32 q^{82} + 80 q^{85} + 112 q^{86} + 8 q^{88} + 72 q^{91} + 8 q^{92} - 112 q^{93} - 80 q^{95} - 88 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bh.a 770.bh 55.l $144$ $6.148$ None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$
770.2.bh.b 770.bh 55.l $144$ $6.148$ None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$

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

\( S_{2}^{\mathrm{old}}(770, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)