Properties

Label 385.2.o
Level $385$
Weight $2$
Character orbit 385.o
Rep. character $\chi_{385}(54,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $88$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 385 = 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 385.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

Trace form

\( 88q - 44q^{4} - 36q^{9} + O(q^{10}) \) \( 88q - 44q^{4} - 36q^{9} - 4q^{11} - 12q^{14} - 4q^{15} - 40q^{16} - 8q^{25} + 24q^{26} - 36q^{31} + 72q^{36} - 8q^{44} + 30q^{45} + 28q^{49} - 28q^{56} - 36q^{59} + 60q^{66} - 42q^{70} + 32q^{71} - 108q^{75} - 90q^{80} + 20q^{81} + 32q^{86} - 72q^{89} + 128q^{91} + 120q^{99} + O(q^{100}) \)

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.o.a \(16\) \(3.074\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) \(\Q(\sqrt{-55}) \) \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{10}-\beta _{14})q^{2}+(\beta _{1}+2\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots\)
385.2.o.b \(72\) \(3.074\) None \(0\) \(0\) \(0\) \(0\)