Properties

Label 385.2.bj
Level $385$
Weight $2$
Character orbit 385.bj
Rep. character $\chi_{385}(8,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $288$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 385 = 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 385.bj (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(385, [\chi])\).

Total New Old
Modular forms 416 288 128
Cusp forms 352 288 64
Eisenstein series 64 0 64

Trace form

\( 288q - 4q^{3} + O(q^{10}) \) \( 288q - 4q^{3} + 4q^{11} - 96q^{12} - 16q^{15} + 72q^{16} - 76q^{20} - 44q^{22} - 16q^{23} - 12q^{25} - 64q^{26} - 4q^{27} - 80q^{30} + 32q^{31} - 32q^{33} - 56q^{36} - 4q^{37} - 16q^{38} + 48q^{45} - 40q^{46} + 16q^{47} + 136q^{48} + 80q^{50} - 80q^{51} + 80q^{52} + 76q^{53} + 112q^{55} - 48q^{56} + 80q^{57} + 32q^{58} - 40q^{60} - 220q^{62} + 16q^{66} + 128q^{67} - 16q^{70} - 72q^{71} - 300q^{72} + 48q^{75} - 8q^{77} - 64q^{78} - 80q^{80} + 60q^{81} + 24q^{82} - 200q^{83} - 40q^{85} - 160q^{86} - 352q^{88} - 36q^{91} + 236q^{92} + 68q^{93} + 80q^{95} - 320q^{96} + 44q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(385, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
385.2.bj.a \(288\) \(3.074\) None \(0\) \(-4\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(385, [\chi])\) into lower level spaces

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