Properties

Label 171.3.p
Level $171$
Weight $3$
Character orbit 171.p
Rep. character $\chi_{171}(46,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $30$
Newform subspaces $6$
Sturm bound $60$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 171.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(60\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

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

Total New Old
Modular forms 88 34 54
Cusp forms 72 30 42
Eisenstein series 16 4 12

Trace form

\( 30 q + 3 q^{2} + 25 q^{4} - 16 q^{7} + O(q^{10}) \) \( 30 q + 3 q^{2} + 25 q^{4} - 16 q^{7} + 10 q^{11} - 6 q^{13} + 84 q^{14} - 43 q^{16} + 14 q^{17} - 51 q^{19} - 16 q^{20} + 9 q^{22} - 38 q^{23} - 41 q^{25} - 28 q^{26} + 48 q^{29} - 39 q^{32} + 54 q^{34} + 68 q^{35} - 188 q^{38} + 144 q^{40} - 183 q^{41} - 38 q^{43} - 13 q^{44} + 18 q^{47} + 18 q^{49} - 222 q^{52} - 78 q^{53} - 48 q^{55} + 44 q^{58} - 15 q^{59} + 34 q^{61} + 346 q^{62} + 86 q^{64} - 147 q^{67} + 260 q^{68} + 186 q^{70} + 390 q^{71} - 25 q^{73} - 78 q^{74} + 351 q^{76} + 132 q^{77} + 420 q^{79} - 452 q^{80} - 197 q^{82} + 454 q^{83} + 254 q^{85} + 60 q^{86} - 498 q^{89} - 252 q^{91} - 58 q^{92} - 448 q^{95} - 675 q^{97} - 687 q^{98} + O(q^{100}) \)

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.p.a 171.p 19.d $2$ $4.659$ \(\Q(\sqrt{-3}) \) None \(-3\) \(0\) \(-4\) \(10\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-4+4\zeta_{6})q^{5}+\cdots\)
171.3.p.b 171.p 19.d $2$ $4.659$ \(\Q(\sqrt{-3}) \) None \(3\) \(0\) \(4\) \(10\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(4-4\zeta_{6})q^{5}+\cdots\)
171.3.p.c 171.p 19.d $6$ $4.659$ 6.0.92607408.1 None \(-3\) \(0\) \(-4\) \(-22\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{4}q^{2}+(1+\beta _{1}+2\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
171.3.p.d 171.p 19.d $6$ $4.659$ 6.0.6967728.1 None \(3\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{5})q^{2}+(-2\beta _{1}-2\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
171.3.p.e 171.p 19.d $6$ $4.659$ 6.0.6967728.1 None \(3\) \(0\) \(2\) \(26\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{3}q^{2}+(-\beta _{1}+\beta _{2}-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
171.3.p.f 171.p 19.d $8$ $4.659$ 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-40\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(3\beta _{2}+\beta _{4}+2\beta _{6})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(171, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)