Properties

Label 567.2.f
Level $567$
Weight $2$
Character orbit 567.f
Rep. character $\chi_{567}(190,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $48$
Newform subspaces $14$
Sturm bound $144$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(144\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

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

Total New Old
Modular forms 168 48 120
Cusp forms 120 48 72
Eisenstein series 48 0 48

Trace form

\( 48q - 24q^{4} + O(q^{10}) \) \( 48q - 24q^{4} - 24q^{16} + 24q^{19} - 12q^{22} - 36q^{25} - 12q^{31} + 48q^{34} + 24q^{37} + 60q^{40} - 12q^{43} - 120q^{46} - 24q^{49} - 36q^{52} + 24q^{55} - 36q^{58} - 24q^{67} + 72q^{73} + 24q^{76} - 12q^{79} + 72q^{82} + 84q^{88} + 24q^{91} + 84q^{94} - 36q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
567.2.f.a \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-1\) \(1\) \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
567.2.f.b \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(1\) \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
567.2.f.c \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(1\) \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
567.2.f.d \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-1\) \(q+2\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
567.2.f.e \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(-1\) \(q+2\zeta_{6}q^{4}+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
567.2.f.f \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(1\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
567.2.f.g \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(2\) \(1\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
567.2.f.h \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(1\) \(1\) \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
567.2.f.i \(4\) \(4.528\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(2\) \(q+\beta _{1}q^{2}+5\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
567.2.f.j \(4\) \(4.528\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+(-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
567.2.f.k \(4\) \(4.528\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+(\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
567.2.f.l \(6\) \(4.528\) 6.0.1156923.1 None \(0\) \(0\) \(-3\) \(-3\) \(q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
567.2.f.m \(6\) \(4.528\) 6.0.1156923.1 None \(0\) \(0\) \(3\) \(-3\) \(q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
567.2.f.n \(8\) \(4.528\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{3}q^{2}+\beta _{4}q^{4}-2\beta _{7}q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots\)

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

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