Properties

Label 770.2.bh
Level $770$
Weight $2$
Character orbit 770.bh
Rep. character $\chi_{770}(57,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $288$
Newform subspaces $2$
Sturm bound $288$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.bh (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
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 1216 288 928
Cusp forms 1088 288 800
Eisenstein series 128 0 128

Trace form

\( 288q + 8q^{3} + O(q^{10}) \) \( 288q + 8q^{3} - 8q^{11} + 32q^{12} + 8q^{15} + 72q^{16} + 8q^{20} + 8q^{22} + 32q^{23} - 16q^{27} - 32q^{31} + 40q^{33} + 88q^{36} - 8q^{37} + 72q^{38} - 96q^{45} - 80q^{46} - 24q^{47} - 8q^{48} - 80q^{50} + 40q^{51} - 80q^{52} - 80q^{53} - 160q^{55} - 160q^{57} - 40q^{60} - 80q^{62} - 48q^{66} - 160q^{67} + 16q^{70} + 96q^{71} - 72q^{75} + 16q^{77} - 32q^{78} + 160q^{81} - 32q^{82} + 80q^{85} + 112q^{86} + 8q^{88} + 72q^{91} + 8q^{92} - 112q^{93} - 80q^{95} - 88q^{97} + O(q^{100}) \)

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.bh.a \(144\) \(6.148\) None \(0\) \(4\) \(0\) \(0\)
770.2.bh.b \(144\) \(6.148\) None \(0\) \(4\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(770, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)