Properties

Label 576.2.i
Level $576$
Weight $2$
Character orbit 576.i
Rep. character $\chi_{576}(193,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $44$
Newform subspaces $14$
Sturm bound $192$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(192\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(576, [\chi])\).

Total New Old
Modular forms 216 52 164
Cusp forms 168 44 124
Eisenstein series 48 8 40

Trace form

\( 44q + 2q^{5} - 4q^{9} + O(q^{10}) \) \( 44q + 2q^{5} - 4q^{9} + 2q^{13} - 8q^{17} - 2q^{21} - 16q^{25} + 2q^{29} + 18q^{33} + 8q^{37} + 6q^{41} + 18q^{45} - 12q^{49} + 56q^{53} - 24q^{57} + 2q^{61} + 18q^{65} + 22q^{69} - 8q^{73} - 26q^{77} - 28q^{81} + 12q^{85} - 40q^{89} - 74q^{93} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
576.2.i.a \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(2\) \(q+(-1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
576.2.i.b \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(4\) \(2\) \(q+(-1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
576.2.i.c \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-3\) \(q+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+\cdots\)
576.2.i.d \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(3\) \(q+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots\)
576.2.i.e \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(-1\) \(q+(-1+2\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
576.2.i.f \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(1\) \(q+(1-2\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
576.2.i.g \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(-2\) \(q+(1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
576.2.i.h \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(4\) \(-2\) \(q+(1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots\)
576.2.i.i \(4\) \(4.599\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(-4\) \(-2\) \(-2\) \(q+(-1+\beta _{3})q^{3}-\beta _{2}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
576.2.i.j \(4\) \(4.599\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-1\) \(-1\) \(-3\) \(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
576.2.i.k \(4\) \(4.599\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}^{3}q^{3}+(-1+\zeta_{12})q^{5}-\zeta_{12}^{2}q^{7}+\cdots\)
576.2.i.l \(4\) \(4.599\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(1\) \(-1\) \(3\) \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
576.2.i.m \(4\) \(4.599\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(4\) \(-2\) \(2\) \(q+(1-\beta _{3})q^{3}+(-1+\beta _{2})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
576.2.i.n \(8\) \(4.599\) 8.0.170772624.1 None \(0\) \(0\) \(-2\) \(0\) \(q+(-\beta _{1}+\beta _{5})q^{3}+(-1+\beta _{4}-\beta _{7})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)