Properties

Label 770.2.o
Level $770$
Weight $2$
Character orbit 770.o
Rep. character $\chi_{770}(439,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $2$
Sturm bound $288$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(17\)

Dimensions

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

Total New Old
Modular forms 304 96 208
Cusp forms 272 96 176
Eisenstein series 32 0 32

Trace form

\( 96q - 48q^{4} - 12q^{5} - 56q^{9} + O(q^{10}) \) \( 96q - 48q^{4} - 12q^{5} - 56q^{9} + 2q^{11} + 4q^{14} + 8q^{15} - 48q^{16} - 12q^{26} + 24q^{31} + 112q^{36} + 2q^{44} + 12q^{45} - 72q^{49} - 8q^{56} - 4q^{60} + 96q^{64} - 48q^{66} - 4q^{70} - 80q^{71} + 180q^{75} + 12q^{80} - 144q^{81} - 24q^{86} + 120q^{89} - 112q^{91} - 116q^{99} + O(q^{100}) \)

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.o.a \(48\) \(6.148\) None \(-24\) \(0\) \(-6\) \(-4\)
770.2.o.b \(48\) \(6.148\) None \(24\) \(0\) \(-6\) \(4\)

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

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