Properties

Label 567.2.g
Level $567$
Weight $2$
Character orbit 567.g
Rep. character $\chi_{567}(109,\cdot)$
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.g (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

\( 60q - 30q^{4} - 3q^{7} + O(q^{10}) \) \( 60q - 30q^{4} - 3q^{7} + 6q^{10} + 9q^{13} - 30q^{16} - 12q^{19} + 48q^{25} - 12q^{28} + 18q^{31} + 3q^{37} + 24q^{43} - 6q^{46} - 27q^{49} - 36q^{52} - 48q^{55} - 48q^{58} - 15q^{61} + 48q^{64} - 3q^{67} - 30q^{70} - 48q^{76} + 45q^{79} - 6q^{82} + 6q^{85} + 36q^{88} - 51q^{91} + 30q^{94} + 9q^{97} + O(q^{100}) \)

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.g.a \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-4\) \(1\) \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-2q^{5}+\cdots\)
567.2.g.b \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-8\) \(1\) \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-4q^{5}+(2+\cdots)q^{7}+\cdots\)
567.2.g.c \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) \(q+2\zeta_{6}q^{4}+(-3+2\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{13}+\cdots\)
567.2.g.d \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(5\) \(q+2\zeta_{6}q^{4}+(3-\zeta_{6})q^{7}+(7-7\zeta_{6})q^{13}+\cdots\)
567.2.g.e \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(8\) \(1\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+4q^{5}+(2-3\zeta_{6})q^{7}+\cdots\)
567.2.g.f \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(4\) \(1\) \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+2q^{5}+(-1+\cdots)q^{7}+\cdots\)
567.2.g.g \(4\) \(4.528\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{2}q^{2}+(-4+4\beta _{1})q^{4}+\beta _{3}q^{5}+\cdots\)
567.2.g.h \(6\) \(4.528\) 6.0.309123.1 None \(-2\) \(0\) \(2\) \(2\) \(q+(-\beta _{1}-\beta _{4}+\beta _{5})q^{2}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
567.2.g.i \(6\) \(4.528\) 6.0.309123.1 None \(2\) \(0\) \(-2\) \(2\) \(q+(1-\beta _{4}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
567.2.g.j \(8\) \(4.528\) 8.0.1767277521.3 None \(-1\) \(0\) \(4\) \(-2\) \(q+(-\beta _{2}-\beta _{6})q^{2}+(-\beta _{5}+\beta _{7})q^{4}+\cdots\)
567.2.g.k \(8\) \(4.528\) 8.0.1767277521.3 None \(1\) \(0\) \(-4\) \(-2\) \(q+(\beta _{2}+\beta _{6})q^{2}+(-\beta _{5}+\beta _{7})q^{4}+(-1+\cdots)q^{5}+\cdots\)
567.2.g.l \(16\) \(4.528\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(-\beta _{5}-\beta _{7}-\beta _{8}-\beta _{12}+\cdots)q^{4}+\cdots\)

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

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