Properties

Label 171.2.f
Level $171$
Weight $2$
Character orbit 171.f
Rep. character $\chi_{171}(64,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $3$
Sturm bound $40$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 48 20 28
Cusp forms 32 16 16
Eisenstein series 16 4 12

Trace form

\( 16 q - 8 q^{4} + 2 q^{5} - 8 q^{7} + 12 q^{8} + 4 q^{10} + 4 q^{11} - 2 q^{14} - 8 q^{16} - 4 q^{17} + 4 q^{19} - 44 q^{20} + 8 q^{22} + 10 q^{23} - 4 q^{25} + 32 q^{26} + 12 q^{28} - 4 q^{29} - 32 q^{31}+ \cdots - 20 q^{98}+O(q^{100}) \) 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.f.a 171.f 19.c $2$ $1.365$ \(\Q(\sqrt{-3}) \) None 57.2.e.a \(1\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+q^{7}+3q^{8}+\cdots\)
171.2.f.b 171.f 19.c $6$ $1.365$ 6.0.954288.1 None 57.2.e.b \(-1\) \(0\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots\)
171.2.f.c 171.f 19.c $8$ $1.365$ 8.0.764411904.5 None 171.2.f.c \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{2}+(-1-\beta _{3}+\beta _{4}-\beta _{6})q^{4}+\cdots\)

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

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