Properties

Label 572.2.i
Level $572$
Weight $2$
Character orbit 572.i
Rep. character $\chi_{572}(133,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $20$
Newform subspaces $3$
Sturm bound $168$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(168\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(572, [\chi])\).

Total New Old
Modular forms 180 20 160
Cusp forms 156 20 136
Eisenstein series 24 0 24

Trace form

\( 20q + 2q^{3} + 4q^{5} - 6q^{7} - 4q^{9} + O(q^{10}) \) \( 20q + 2q^{3} + 4q^{5} - 6q^{7} - 4q^{9} + 12q^{13} + 16q^{15} - 2q^{17} + 10q^{19} - 4q^{21} - 14q^{23} + 24q^{25} - 40q^{27} - 10q^{29} + 20q^{31} + 8q^{35} + 4q^{37} + 24q^{39} + 2q^{41} - 14q^{43} - 16q^{45} + 8q^{47} - 44q^{51} + 4q^{53} + 64q^{57} - 8q^{61} + 10q^{63} - 26q^{65} + 6q^{67} + 26q^{69} + 2q^{71} - 64q^{73} + 42q^{75} - 16q^{77} + 16q^{79} - 18q^{81} - 12q^{83} - 30q^{85} - 12q^{87} + 10q^{89} - 10q^{91} - 46q^{93} + 12q^{95} + 46q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(572, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
572.2.i.a \(4\) \(4.567\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(-4\) \(-2\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{5}+(-1+\zeta_{12}+\cdots)q^{7}+\cdots\)
572.2.i.b \(6\) \(4.567\) 6.0.309123.1 None \(0\) \(-1\) \(6\) \(-5\) \(q+(\beta _{1}-\beta _{5})q^{3}+(1+\beta _{1}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
572.2.i.c \(10\) \(4.567\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(1\) \(2\) \(1\) \(q+\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}-\beta _{5})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(572, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(572, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(286, [\chi])\)\(^{\oplus 2}\)