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Properties

Label 567.2.a
Level $567$
Weight $2$
Character orbit 567.a
Rep. character $\chi_{567}(1,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $9$
Sturm bound $144$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(567))\).

Total New Old
Modular forms 84 24 60
Cusp forms 61 24 37
Eisenstein series 23 0 23

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(7\)FrickeDim
\(+\)\(+\)$+$\(5\)
\(+\)\(-\)$-$\(9\)
\(-\)\(+\)$-$\(7\)
\(-\)\(-\)$+$\(3\)
Plus space\(+\)\(8\)
Minus space\(-\)\(16\)

Trace form

\( 24 q + 24 q^{4} + O(q^{10}) \) \( 24 q + 24 q^{4} + 12 q^{10} + 12 q^{13} + 36 q^{16} - 12 q^{19} + 24 q^{25} + 12 q^{28} - 12 q^{31} - 24 q^{34} + 24 q^{37} + 12 q^{40} - 12 q^{43} - 12 q^{46} + 24 q^{49} - 12 q^{55} - 12 q^{58} + 36 q^{61} - 12 q^{64} - 24 q^{73} - 60 q^{76} + 12 q^{79} - 24 q^{82} + 48 q^{85} - 48 q^{88} - 12 q^{91} - 84 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(567))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 7
567.2.a.a 567.a 1.a $1$ $4.528$ \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}-q^{7}+3q^{8}-q^{10}+\cdots\)
567.2.a.b 567.a 1.a $1$ $4.528$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}-q^{7}-3q^{8}-q^{10}+\cdots\)
567.2.a.c 567.a 1.a $3$ $4.528$ \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(-3\) \(3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
567.2.a.d 567.a 1.a $3$ $4.528$ 3.3.321.1 None \(-1\) \(0\) \(-5\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{2})q^{5}+\cdots\)
567.2.a.e 567.a 1.a $3$ $4.528$ 3.3.621.1 None \(0\) \(0\) \(-3\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
567.2.a.f 567.a 1.a $3$ $4.528$ 3.3.621.1 None \(0\) \(0\) \(3\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
567.2.a.g 567.a 1.a $3$ $4.528$ 3.3.321.1 None \(1\) \(0\) \(5\) \(-3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(2+\beta _{2})q^{5}+\cdots\)
567.2.a.h 567.a 1.a $3$ $4.528$ \(\Q(\zeta_{18})^+\) None \(3\) \(0\) \(3\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
567.2.a.i 567.a 1.a $4$ $4.528$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}-\beta _{2}q^{4}-2\beta _{1}q^{5}-q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(567))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(567)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 2}\)