Properties

Label 135.1.d
Level $135$
Weight $1$
Character orbit 135.d
Rep. character $\chi_{135}(134,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $18$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 135.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(135, [\chi])\).

Total New Old
Modular forms 8 2 6
Cusp forms 2 2 0
Eisenstein series 6 0 6

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q + O(q^{10}) \) \( 2 q - 2 q^{10} - 2 q^{16} - 2 q^{19} + 2 q^{25} - 2 q^{31} + 2 q^{34} + 2 q^{40} + 2 q^{46} + 2 q^{49} - 2 q^{61} + 2 q^{64} - 2 q^{79} - 2 q^{85} - 4 q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(135, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
135.1.d.a 135.d 15.d $1$ $0.067$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-15}) \) None 135.1.d.a \(-1\) \(0\) \(1\) \(0\) \(q-q^{2}+q^{5}+q^{8}-q^{10}-q^{16}-q^{17}+\cdots\)
135.1.d.b 135.d 15.d $1$ $0.067$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-15}) \) None 135.1.d.a \(1\) \(0\) \(-1\) \(0\) \(q+q^{2}-q^{5}-q^{8}-q^{10}-q^{16}+q^{17}+\cdots\)