Properties

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

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 572.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(572))\) into irreducible Hecke orbits

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

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