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Properties

Label 171.2.d
Level $171$
Weight $2$
Character orbit 171.d
Rep. character $\chi_{171}(170,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $40$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 171.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(40\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(171, [\chi])\).

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

Trace form

\( 8 q + 4 q^{4} - 8 q^{7} + 12 q^{16} - 12 q^{19} - 8 q^{25} - 24 q^{28} + 12 q^{43} + 36 q^{49} - 20 q^{55} + 40 q^{58} + 32 q^{61} - 84 q^{64} + 68 q^{73} - 36 q^{76} - 40 q^{82} - 76 q^{85}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(171, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
171.2.d.a 171.d 57.d $4$ $1.365$ \(\Q(\sqrt{-2}, \sqrt{19})\) \(\Q(\sqrt{-19}) \) 171.2.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{4}+\beta _{1}q^{5}+\beta _{3}q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
171.2.d.b 171.d 57.d $4$ $1.365$ \(\Q(\sqrt{-2}, \sqrt{5})\) None 171.2.d.b \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+3q^{4}-\beta _{1}q^{5}-2q^{7}-\beta _{3}q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(171, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(171, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)