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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
770.2.bc.a \(80\) \(6.148\) None \(0\) \(0\) \(0\) \(0\)
770.2.bc.b \(80\) \(6.148\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(770, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)