↑

Properties

Label 770.2.bc
Level $770$
Weight $2$
Character orbit 770.bc
Rep. character $\chi_{770}(243,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $160$
Newform subspaces $2$
Sturm bound $288$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.bc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
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 608 160 448
Cusp forms 544 160 384
Eisenstein series 64 0 64

Trace form

\( 160 q + O(q^{10}) \) \( 160 q - 48 q^{15} + 80 q^{16} + 72 q^{17} + 16 q^{18} + 56 q^{21} - 24 q^{30} - 48 q^{31} + 24 q^{35} - 144 q^{36} - 48 q^{38} - 48 q^{42} - 64 q^{43} - 72 q^{45} + 24 q^{46} + 16 q^{53} - 8 q^{56} + 80 q^{57} + 32 q^{58} - 16 q^{60} + 24 q^{61} + 136 q^{63} - 16 q^{65} - 16 q^{67} + 72 q^{68} - 16 q^{70} - 64 q^{71} + 16 q^{72} - 96 q^{73} - 48 q^{75} - 32 q^{78} + 64 q^{81} + 48 q^{82} - 96 q^{85} - 24 q^{86} + 72 q^{87} + 64 q^{91} - 8 q^{93} - 16 q^{95} - 24 q^{96} - 112 q^{98} + O(q^{100}) \)

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.bc.a 770.bc 35.k $80$ $6.148$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
770.2.bc.b 770.bc 35.k $80$ $6.148$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(770, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)