Properties

Label 770.2.r
Level $770$
Weight $2$
Character orbit 770.r
Rep. character $\chi_{770}(529,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $2$
Sturm bound $288$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 304 80 224
Cusp forms 272 80 192
Eisenstein series 32 0 32

Trace form

\( 80q + 40q^{4} + 8q^{6} + 44q^{9} + O(q^{10}) \) \( 80q + 40q^{4} + 8q^{6} + 44q^{9} + 8q^{14} + 40q^{15} - 40q^{16} + 16q^{19} - 12q^{21} + 4q^{24} - 8q^{25} - 24q^{26} - 56q^{29} - 20q^{30} + 24q^{31} - 32q^{34} - 20q^{35} + 88q^{36} + 32q^{39} - 24q^{41} - 12q^{45} - 12q^{46} - 36q^{49} + 32q^{50} + 24q^{51} + 4q^{54} + 4q^{56} + 16q^{59} + 20q^{60} - 28q^{61} - 80q^{64} + 12q^{65} - 16q^{66} + 56q^{69} - 16q^{70} - 48q^{71} + 24q^{74} - 28q^{75} + 32q^{76} + 24q^{79} - 72q^{81} + 48q^{84} + 48q^{85} + 4q^{86} + 68q^{89} - 24q^{90} - 64q^{91} - 56q^{94} + 4q^{95} - 4q^{96} + O(q^{100}) \)

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.r.a \(40\) \(6.148\) None \(0\) \(0\) \(0\) \(0\)
770.2.r.b \(40\) \(6.148\) None \(0\) \(0\) \(0\) \(0\)

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

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