Properties

Label 567.2.i
Level $567$
Weight $2$
Character orbit 567.i
Rep. character $\chi_{567}(215,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $60$
Newform subspaces $7$
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.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 7 \)
Sturm bound: \(144\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(11\), \(13\)

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

\( 60q - 52q^{4} + 7q^{7} + O(q^{10}) \) \( 60q - 52q^{4} + 7q^{7} - 6q^{10} + 15q^{13} + 44q^{16} - 6q^{19} + 8q^{22} - 24q^{25} - 20q^{28} - 12q^{34} - 7q^{37} - 12q^{40} - 16q^{43} + 2q^{46} - 15q^{49} - 78q^{52} + 32q^{58} - 32q^{64} + 6q^{67} - 18q^{70} - 6q^{73} + 36q^{76} + 78q^{79} - 18q^{82} - 18q^{85} - 2q^{88} + 45q^{91} + 15q^{97} + O(q^{100}) \)

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.i.a \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-5\) \(q+2q^{4}+(-2-\zeta_{6})q^{7}+(8-4\zeta_{6})q^{13}+\cdots\)
567.2.i.b \(2\) \(4.528\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4\) \(q+2q^{4}+(1+2\zeta_{6})q^{7}+(2-\zeta_{6})q^{13}+\cdots\)
567.2.i.c \(4\) \(4.528\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(10\) \(q+\beta _{3}q^{2}-3q^{4}+(2+\beta _{2})q^{7}-\beta _{3}q^{8}+\cdots\)
567.2.i.d \(4\) \(4.528\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{3}q^{2}+(\beta _{1}+\beta _{3})q^{5}+(-3+2\beta _{2}+\cdots)q^{7}+\cdots\)
567.2.i.e \(4\) \(4.528\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-2\) \(q+\beta _{3}q^{2}+(-\beta _{1}-\beta _{3})q^{5}+(1-3\beta _{2}+\cdots)q^{7}+\cdots\)
567.2.i.f \(12\) \(4.528\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{11}q^{2}+(-1+\beta _{7})q^{4}-\beta _{6}q^{5}+\cdots\)
567.2.i.g \(32\) \(4.528\) None \(0\) \(0\) \(0\) \(4\)

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

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