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Properties

Label 272.3.bh
Level $272$
Weight $3$
Character orbit 272.bh
Rep. character $\chi_{272}(65,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $136$
Newform subspaces $7$
Sturm bound $108$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 272 = 2^{4} \cdot 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 272.bh (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 7 \)
Sturm bound: \(108\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(272, [\chi])\).

Total New Old
Modular forms 624 152 472
Cusp forms 528 136 392
Eisenstein series 96 16 80

Trace form

\( 136 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + O(q^{10}) \) \( 136 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{31} + 16 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} + 8 q^{51} - 120 q^{53} + 584 q^{55} + 152 q^{57} + 392 q^{59} - 200 q^{61} + 584 q^{63} + 72 q^{65} + 112 q^{69} - 184 q^{71} - 248 q^{73} - 1144 q^{75} + 312 q^{77} - 568 q^{79} - 232 q^{81} - 760 q^{83} + 136 q^{85} + 8 q^{87} - 8 q^{89} + 8 q^{91} - 8 q^{93} + 8 q^{95} - 8 q^{97} - 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(272, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
272.3.bh.a 272.bh 17.e $8$ $7.411$ \(\Q(\zeta_{16})\) None 34.3.e.a \(0\) \(-8\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(-1-\zeta_{16}+\zeta_{16}^{2}+\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{3}+\cdots\)
272.3.bh.b 272.bh 17.e $8$ $7.411$ \(\Q(\zeta_{16})\) None 17.3.e.b \(0\) \(0\) \(-24\) \(16\) $\mathrm{SU}(2)[C_{16}]$ \(q+(-2\zeta_{16}^{2}-\zeta_{16}^{3}+\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{3}+\cdots\)
272.3.bh.c 272.bh 17.e $8$ $7.411$ \(\Q(\zeta_{16})\) None 17.3.e.a \(0\) \(8\) \(16\) \(-8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(1+\zeta_{16}+\zeta_{16}^{3}-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{3}+\cdots\)
272.3.bh.d 272.bh 17.e $16$ $7.411$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 34.3.e.b \(0\) \(8\) \(0\) \(8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(\beta _{3}+\beta _{5}+\beta _{13})q^{3}+(-1-\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)
272.3.bh.e 272.bh 17.e $24$ $7.411$ None 68.3.j.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
272.3.bh.f 272.bh 17.e $32$ $7.411$ None 136.3.t.a \(0\) \(8\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{16}]$
272.3.bh.g 272.bh 17.e $40$ $7.411$ None 136.3.t.b \(0\) \(-8\) \(0\) \(8\) $\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{3}^{\mathrm{old}}(272, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(272, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 2}\)