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Properties

Label 171.3.r
Level $171$
Weight $3$
Character orbit 171.r
Rep. character $\chi_{171}(26,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $3$
Sturm bound $60$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 171.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(60\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(171, [\chi])\).

Total New Old
Modular forms 88 24 64
Cusp forms 72 24 48
Eisenstein series 16 0 16

Trace form

\( 24 q + 12 q^{4} + 16 q^{7} + O(q^{10}) \) \( 24 q + 12 q^{4} + 16 q^{7} + 20 q^{10} + 20 q^{13} - 12 q^{16} + 36 q^{19} + 16 q^{22} - 40 q^{25} + 32 q^{28} - 56 q^{31} - 76 q^{34} - 128 q^{37} - 120 q^{40} + 84 q^{43} - 128 q^{46} - 176 q^{49} - 32 q^{52} + 60 q^{55} + 320 q^{58} + 40 q^{61} + 144 q^{64} + 252 q^{67} + 120 q^{70} - 120 q^{73} + 348 q^{76} + 148 q^{79} - 460 q^{82} + 480 q^{85} - 888 q^{88} - 244 q^{91} - 720 q^{94} - 704 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(171, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
171.3.r.a 171.r 57.h $4$ $4.659$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-6\) \(0\) \(12\) \(20\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{2})q^{2}-\beta _{2}q^{4}+(2-\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
171.3.r.b 171.r 57.h $4$ $4.659$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(6\) \(0\) \(-12\) \(20\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\beta _{2})q^{2}+(-1+\beta _{2})q^{4}+(-4+\cdots)q^{5}+\cdots\)
171.3.r.c 171.r 57.h $16$ $4.659$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-2\beta _{2}+\beta _{6}+\beta _{8}-\beta _{9}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(171, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(171, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)