Properties

Label 770.2.bd
Level $770$
Weight $2$
Character orbit 770.bd
Rep. character $\chi_{770}(263,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $192$
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.bd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{12})\)
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 608 192 416
Cusp forms 544 192 352
Eisenstein series 64 0 64

Trace form

\( 192q + 8q^{5} + O(q^{10}) \) \( 192q + 8q^{5} + 4q^{11} + 16q^{15} + 96q^{16} + 24q^{22} - 8q^{23} + 24q^{25} - 8q^{26} - 16q^{33} - 160q^{36} - 40q^{37} - 40q^{42} + 32q^{45} - 40q^{47} + 40q^{53} + 8q^{55} + 16q^{56} + 32q^{58} - 48q^{67} - 72q^{70} + 32q^{71} - 48q^{75} - 72q^{77} - 8q^{80} + 64q^{81} + 16q^{82} - 12q^{88} - 112q^{91} - 16q^{92} + 80q^{93} - 64q^{97} + O(q^{100}) \)

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.bd.a \(192\) \(6.148\) None \(0\) \(0\) \(8\) \(0\)

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

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