Properties

Label 770.2.bi
Level $770$
Weight $2$
Character orbit 770.bi
Rep. character $\chi_{770}(27,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $384$
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.bi (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{20})\)
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 1216 384 832
Cusp forms 1088 384 704
Eisenstein series 128 0 128

Trace form

\( 384q - 4q^{7} + O(q^{10}) \) \( 384q - 4q^{7} + 24q^{15} + 96q^{16} + 16q^{22} + 16q^{23} - 40q^{25} + 4q^{28} + 16q^{30} - 32q^{35} + 80q^{36} - 64q^{37} + 44q^{42} - 80q^{43} - 16q^{46} - 64q^{50} - 136q^{51} + 80q^{53} + 8q^{56} - 112q^{57} - 96q^{58} + 68q^{63} - 272q^{65} + 160q^{67} - 8q^{70} + 16q^{71} + 96q^{77} + 24q^{81} - 80q^{85} - 16q^{88} - 84q^{91} + 16q^{92} + 88q^{93} - 184q^{95} - 32q^{98} + O(q^{100}) \)

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.bi.a \(384\) \(6.148\) None \(0\) \(0\) \(0\) \(-4\)

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

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