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Properties

Label 171.3.ba
Level $171$
Weight $3$
Character orbit 171.ba
Rep. character $\chi_{171}(10,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $96$
Newform subspaces $5$
Sturm bound $60$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 171.ba (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 5 \)
Sturm bound: \(60\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 264 108 156
Cusp forms 216 96 120
Eisenstein series 48 12 36

Trace form

\( 96 q + 6 q^{2} - 12 q^{4} + 6 q^{5} + 6 q^{7} + 9 q^{8} + O(q^{10}) \) \( 96 q + 6 q^{2} - 12 q^{4} + 6 q^{5} + 6 q^{7} + 9 q^{8} - 9 q^{10} - 12 q^{11} + 27 q^{13} - 3 q^{14} - 24 q^{16} + 63 q^{17} + 54 q^{19} - 66 q^{20} - 126 q^{22} + 54 q^{23} + 108 q^{25} - 117 q^{26} + 348 q^{28} + 105 q^{29} + 99 q^{31} + 273 q^{32} + 72 q^{34} - 204 q^{35} + 156 q^{38} - 378 q^{40} + 120 q^{41} - 81 q^{43} - 441 q^{44} - 774 q^{46} - 411 q^{47} - 342 q^{49} - 774 q^{50} - 51 q^{52} - 21 q^{53} - 78 q^{55} + 108 q^{58} + 159 q^{59} - 354 q^{61} + 576 q^{62} + 567 q^{64} + 954 q^{65} - 207 q^{67} + 480 q^{68} - 231 q^{70} + 168 q^{71} + 432 q^{73} + 615 q^{74} - 486 q^{76} - 318 q^{77} + 177 q^{79} + 1113 q^{80} + 483 q^{82} - 222 q^{83} + 720 q^{85} - 456 q^{86} + 1467 q^{88} - 114 q^{89} - 33 q^{91} - 1536 q^{92} - 57 q^{95} + 9 q^{97} - 1077 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
171.3.ba.a 171.ba 19.f $6$ $4.659$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) 171.3.ba.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{18}]$ \(q-4\zeta_{18}q^{4}+(-3\zeta_{18}+8\zeta_{18}^{2}+8\zeta_{18}^{4}+\cdots)q^{7}+\cdots\)
171.3.ba.b 171.ba 19.f $12$ $4.659$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 19.3.f.a \(6\) \(0\) \(6\) \(6\) $\mathrm{SU}(2)[C_{18}]$ \(q+(1-\beta _{4}+\beta _{6}-\beta _{9})q^{2}+(-\beta _{5}-\beta _{8}+\cdots)q^{4}+\cdots\)
171.3.ba.c 171.ba 19.f $18$ $4.659$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None 57.3.k.a \(-9\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{18}]$ \(q+(\beta _{3}+\beta _{8}+\beta _{10}+\beta _{15}+\beta _{16})q^{2}+\cdots\)
171.3.ba.d 171.ba 19.f $24$ $4.659$ None 57.3.k.b \(9\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{18}]$
171.3.ba.e 171.ba 19.f $36$ $4.659$ None 171.3.ba.e \(0\) \(0\) \(0\) \(18\) $\mathrm{SU}(2)[C_{18}]$

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

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