Properties

Label 572.2.a
Level $572$
Weight $2$
Character orbit 572.a
Rep. character $\chi_{572}(1,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $5$
Sturm bound $168$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(168\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(572))\).

Total New Old
Modular forms 90 10 80
Cusp forms 79 10 69
Eisenstein series 11 0 11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(11\)\(13\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(5\)
Minus space\(-\)\(5\)

Trace form

\( 10q - 2q^{3} + 2q^{5} + 16q^{9} + O(q^{10}) \) \( 10q - 2q^{3} + 2q^{5} + 16q^{9} + 2q^{11} - 10q^{15} - 16q^{17} - 4q^{19} + 4q^{21} - 10q^{23} - 2q^{27} - 8q^{29} - 14q^{31} + 2q^{33} + 4q^{35} + 2q^{37} + 4q^{41} + 8q^{43} + 4q^{45} - 8q^{47} + 30q^{49} - 4q^{51} - 16q^{53} - 6q^{55} - 28q^{57} + 18q^{59} + 20q^{61} + 8q^{63} - 4q^{65} - 6q^{67} + 10q^{69} - 26q^{71} - 20q^{73} + 12q^{75} - 4q^{77} - 4q^{79} - 6q^{81} - 36q^{85} + 12q^{87} + 2q^{89} + 4q^{91} + 10q^{93} + 60q^{95} + 2q^{97} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(572))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 11 13
572.2.a.a \(1\) \(4.567\) \(\Q\) None \(0\) \(1\) \(3\) \(2\) \(-\) \(-\) \(-\) \(q+q^{3}+3q^{5}+2q^{7}-2q^{9}+q^{11}+\cdots\)
572.2.a.b \(2\) \(4.567\) \(\Q(\sqrt{13}) \) None \(0\) \(-3\) \(0\) \(-3\) \(-\) \(+\) \(-\) \(q+(-1-\beta )q^{3}+(-2+\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
572.2.a.c \(2\) \(4.567\) \(\Q(\sqrt{21}) \) None \(0\) \(1\) \(-4\) \(3\) \(-\) \(-\) \(-\) \(q+\beta q^{3}-2q^{5}+(1+\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
572.2.a.d \(2\) \(4.567\) \(\Q(\sqrt{21}) \) None \(0\) \(1\) \(4\) \(5\) \(-\) \(+\) \(+\) \(q+\beta q^{3}+2q^{5}+(3-\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
572.2.a.e \(3\) \(4.567\) 3.3.229.1 None \(0\) \(-2\) \(-1\) \(-7\) \(-\) \(-\) \(+\) \(q+(-1-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(572))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(572)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 2}\)