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Properties

Label 387.2.d
Level $387$
Weight $2$
Character orbit 387.d
Rep. character $\chi_{387}(386,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $88$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 387.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 129 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(88\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(387, [\chi])\).

Total New Old
Modular forms 48 16 32
Cusp forms 40 16 24
Eisenstein series 8 0 8

Trace form

\( 16 q + 20 q^{4} + O(q^{10}) \) \( 16 q + 20 q^{4} - 16 q^{10} - 24 q^{13} + 36 q^{16} + 16 q^{25} - 8 q^{31} - 8 q^{40} - 28 q^{43} - 8 q^{49} - 96 q^{52} + 8 q^{58} + 60 q^{64} + 16 q^{67} - 64 q^{79} + 52 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(387, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
387.2.d.a 387.d 129.d $4$ $3.090$ \(\Q(\sqrt{-2}, \sqrt{43})\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{4}+\beta _{1}q^{11}+\beta _{3}q^{13}+4q^{16}+\cdots\)
387.2.d.b 387.d 129.d $12$ $3.090$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(2+\beta _{3}+\beta _{6})q^{4}+\beta _{1}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(387, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(387, [\chi]) \cong \)