Properties

Label 385.2.u
Level $385$
Weight $2$
Character orbit 385.u
Rep. character $\chi_{385}(131,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
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.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{6})\)
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 64 40
Cusp forms 88 64 24
Eisenstein series 16 0 16

Trace form

\( 64q + 28q^{4} + 36q^{9} + O(q^{10}) \) \( 64q + 28q^{4} + 36q^{9} - 20q^{14} - 8q^{15} - 48q^{16} + 16q^{22} + 20q^{23} + 32q^{25} - 60q^{26} + 24q^{33} + 16q^{36} - 8q^{37} + 84q^{38} - 132q^{42} + 12q^{44} + 12q^{47} + 12q^{49} + 20q^{53} + 32q^{56} + 24q^{58} + 36q^{59} - 44q^{60} - 120q^{64} + 12q^{66} + 44q^{67} + 16q^{70} - 72q^{71} + 44q^{77} - 120q^{78} - 24q^{80} - 48q^{81} - 96q^{82} + 76q^{86} + 64q^{88} + 60q^{89} - 108q^{91} - 40q^{92} - 68q^{93} - 64q^{99} + O(q^{100}) \)

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.u.a \(64\) \(3.074\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(385, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)