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Properties

Label 567.3.r
Level $567$
Weight $3$
Character orbit 567.r
Rep. character $\chi_{567}(134,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $6$
Sturm bound $216$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 567.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(216\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(567, [\chi])\).

Total New Old
Modular forms 312 96 216
Cusp forms 264 96 168
Eisenstein series 48 0 48

Trace form

\( 96 q + 96 q^{4} + O(q^{10}) \) \( 96 q + 96 q^{4} - 192 q^{16} + 48 q^{19} + 48 q^{22} + 252 q^{25} - 60 q^{31} - 156 q^{34} - 168 q^{37} + 300 q^{40} + 120 q^{43} + 840 q^{46} - 336 q^{49} + 36 q^{52} + 264 q^{55} - 180 q^{58} - 2592 q^{64} - 12 q^{67} + 144 q^{73} - 636 q^{76} + 12 q^{79} + 360 q^{82} - 108 q^{85} - 408 q^{88} - 168 q^{91} + 1068 q^{94} + 252 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(567, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
567.3.r.a 567.r 9.d $8$ $15.450$ 8.0.\(\cdots\).5 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(\beta _{3}+\beta _{6})q^{4}-2\beta _{5}q^{5}-\beta _{6}q^{7}+\cdots\)
567.3.r.b 567.r 9.d $8$ $15.450$ 8.0.\(\cdots\).5 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(\beta _{3}+\beta _{6})q^{4}+\beta _{7}q^{5}-\beta _{6}q^{7}+\cdots\)
567.3.r.c 567.r 9.d $8$ $15.450$ 8.0.\(\cdots\).8 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{4}q^{2}+(3-2\beta _{1}+3\beta _{3})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)
567.3.r.d 567.r 9.d $8$ $15.450$ 8.0.\(\cdots\).53 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}-\beta _{3})q^{2}+(6+6\beta _{2}-\beta _{6})q^{4}+\cdots\)
567.3.r.e 567.r 9.d $16$ $15.450$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{8}q^{2}+(1-\beta _{2}+\beta _{5}-\beta _{7}+\beta _{15})q^{4}+\cdots\)
567.3.r.f 567.r 9.d $48$ $15.450$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(567, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(567, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)