Properties

Label 385.2.k
Level $385$
Weight $2$
Character orbit 385.k
Rep. character $\chi_{385}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $72$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
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 104 72 32
Cusp forms 88 72 16
Eisenstein series 16 0 16

Trace form

\( 72q + 4q^{3} + O(q^{10}) \) \( 72q + 4q^{3} - 4q^{11} + 16q^{12} + 16q^{15} - 72q^{16} - 24q^{20} + 44q^{22} - 4q^{23} - 28q^{25} + 64q^{26} + 4q^{27} - 32q^{31} + 32q^{33} - 104q^{36} + 4q^{37} - 104q^{38} + 12q^{45} - 16q^{47} + 24q^{48} - 16q^{53} - 32q^{55} + 48q^{56} - 32q^{58} + 200q^{60} + 64q^{66} - 68q^{67} + 16q^{70} + 72q^{71} - 48q^{75} + 8q^{77} - 56q^{78} + 80q^{80} - 80q^{81} - 104q^{82} - 80q^{86} + 32q^{88} - 24q^{91} - 136q^{92} - 68q^{93} - 44q^{97} + O(q^{100}) \)

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.k.a \(72\) \(3.074\) None \(0\) \(4\) \(0\) \(0\)

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

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