Properties

Label 1215.1.d
Level $1215$
Weight $1$
Character orbit 1215.d
Rep. character $\chi_{1215}(1214,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $162$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1215 = 3^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1215.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(162\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1215, [\chi])\).

Total New Old
Modular forms 30 6 24
Cusp forms 12 6 6
Eisenstein series 18 0 18

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q + 6 q^{4} + O(q^{10}) \) \( 6 q + 6 q^{4} + 6 q^{16} + 6 q^{25} - 6 q^{34} - 6 q^{40} - 6 q^{46} + 6 q^{49} - 6 q^{76} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1215, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1215.1.d.a 1215.d 15.d $3$ $0.606$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(-3\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{8}+\cdots\)
1215.1.d.b 1215.d 15.d $3$ $0.606$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(3\) \(0\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1-\beta _{1}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1215, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1215, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 3}\)