Properties

Label 528.2.a
Level $528$
Weight $2$
Character orbit 528.a
Rep. character $\chi_{528}(1,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $10$
Sturm bound $192$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 528.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(192\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(528))\).

Total New Old
Modular forms 108 10 98
Cusp forms 85 10 75
Eisenstein series 23 0 23

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

\(2\)\(3\)\(11\)FrickeDim
\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(-\)$-$\(2\)
\(+\)\(-\)\(+\)$-$\(1\)
\(-\)\(+\)\(+\)$-$\(2\)
\(-\)\(+\)\(-\)$+$\(1\)
\(-\)\(-\)\(+\)$+$\(1\)
\(-\)\(-\)\(-\)$-$\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(7\)

Trace form

\( 10 q - 2 q^{3} + 4 q^{5} - 4 q^{7} + 10 q^{9} + O(q^{10}) \) \( 10 q - 2 q^{3} + 4 q^{5} - 4 q^{7} + 10 q^{9} + 4 q^{13} + 4 q^{15} - 4 q^{17} + 4 q^{19} + 6 q^{25} - 2 q^{27} + 4 q^{29} + 16 q^{31} + 24 q^{35} + 4 q^{37} - 4 q^{39} - 4 q^{41} - 4 q^{43} + 4 q^{45} + 24 q^{47} + 2 q^{49} + 8 q^{51} + 4 q^{53} + 8 q^{55} - 8 q^{57} + 16 q^{59} - 12 q^{61} - 4 q^{63} - 24 q^{65} + 8 q^{67} - 16 q^{69} - 8 q^{71} - 28 q^{73} - 14 q^{75} - 20 q^{79} + 10 q^{81} - 24 q^{83} - 8 q^{85} - 12 q^{89} - 40 q^{91} - 24 q^{95} - 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(528))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 11
528.2.a.a 528.a 1.a $1$ $4.216$ \(\Q\) None \(0\) \(-1\) \(-4\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}+2q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
528.2.a.b 528.a 1.a $1$ $4.216$ \(\Q\) None \(0\) \(-1\) \(-2\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-4q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
528.2.a.c 528.a 1.a $1$ $4.216$ \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}-q^{11}-2q^{17}+\cdots\)
528.2.a.d 528.a 1.a $1$ $4.216$ \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
528.2.a.e 528.a 1.a $1$ $4.216$ \(\Q\) None \(0\) \(-1\) \(2\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+2q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
528.2.a.f 528.a 1.a $1$ $4.216$ \(\Q\) None \(0\) \(-1\) \(4\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}+2q^{7}+q^{9}+q^{11}-4q^{15}+\cdots\)
528.2.a.g 528.a 1.a $1$ $4.216$ \(\Q\) None \(0\) \(1\) \(-2\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-4q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
528.2.a.h 528.a 1.a $1$ $4.216$ \(\Q\) None \(0\) \(1\) \(2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-2q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
528.2.a.i 528.a 1.a $1$ $4.216$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{9}-q^{11}+2q^{13}+\cdots\)
528.2.a.j 528.a 1.a $1$ $4.216$ \(\Q\) None \(0\) \(1\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+4q^{7}+q^{9}+q^{11}-6q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(528))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(528)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 2}\)