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Properties

Label 567.2.h
Level $567$
Weight $2$
Character orbit 567.h
Rep. character $\chi_{567}(298,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $60$
Newform subspaces $12$
Sturm bound $144$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.h (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
Sturm bound: \(144\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(567, [\chi])\).

Total New Old
Modular forms 168 68 100
Cusp forms 120 60 60
Eisenstein series 48 8 40

Trace form

\( 60 q + 60 q^{4} - 3 q^{7} + O(q^{10}) \) \( 60 q + 60 q^{4} - 3 q^{7} + 6 q^{10} + 9 q^{13} + 60 q^{16} - 12 q^{19} - 24 q^{25} - 12 q^{28} - 36 q^{31} + 3 q^{37} + 24 q^{43} - 6 q^{46} + 9 q^{49} + 18 q^{52} - 48 q^{55} + 24 q^{58} + 30 q^{61} + 48 q^{64} + 6 q^{67} - 66 q^{70} - 48 q^{76} - 90 q^{79} - 6 q^{82} + 6 q^{85} - 18 q^{88} - 51 q^{91} - 60 q^{94} + 9 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(567, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
567.2.h.a 567.h 63.h $2$ $4.528$ \(\Q(\sqrt{-3}) \) None \(-4\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-2q^{2}+2q^{4}+(-2+2\zeta_{6})q^{5}+(3+\cdots)q^{7}+\cdots\)
567.2.h.b 567.h 63.h $2$ $4.528$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-4\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}-q^{4}+(-4+4\zeta_{6})q^{5}+(-3+\cdots)q^{7}+\cdots\)
567.2.h.c 567.h 63.h $2$ $4.528$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) $\mathrm{U}(1)[D_{3}]$ \(q-2q^{4}+(-1-2\zeta_{6})q^{7}+7\zeta_{6}q^{13}+\cdots\)
567.2.h.d 567.h 63.h $2$ $4.528$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(5\) $\mathrm{U}(1)[D_{3}]$ \(q-2q^{4}+(2+\zeta_{6})q^{7}-2\zeta_{6}q^{13}+4q^{16}+\cdots\)
567.2.h.e 567.h 63.h $2$ $4.528$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(4\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}-q^{4}+(4-4\zeta_{6})q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
567.2.h.f 567.h 63.h $2$ $4.528$ \(\Q(\sqrt{-3}) \) None \(4\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+2q^{2}+2q^{4}+(2-2\zeta_{6})q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
567.2.h.g 567.h 63.h $4$ $4.528$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{3}q^{2}+4q^{4}+\beta _{2}q^{5}+(3-\beta _{1})q^{7}+\cdots\)
567.2.h.h 567.h 63.h $6$ $4.528$ 6.0.309123.1 None \(-4\) \(0\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1})q^{2}+(2+\beta _{1}+\beta _{3})q^{4}+\cdots\)
567.2.h.i 567.h 63.h $6$ $4.528$ 6.0.309123.1 None \(4\) \(0\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1})q^{2}+(2+\beta _{1}+\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)
567.2.h.j 567.h 63.h $8$ $4.528$ 8.0.1767277521.3 None \(-2\) \(0\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(1+\beta _{1})q^{4}+(1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
567.2.h.k 567.h 63.h $8$ $4.528$ 8.0.1767277521.3 None \(2\) \(0\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(1+\beta _{1})q^{4}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
567.2.h.l 567.h 63.h $16$ $4.528$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{15}q^{2}+(1-\beta _{3}+\beta _{5}+\beta _{7}+\beta _{9}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(567, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(567, [\chi]) \cong \)