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Properties

Label 528.3.l
Level $528$
Weight $3$
Character orbit 528.l
Rep. character $\chi_{528}(463,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $4$
Sturm bound $288$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 528.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(528, [\chi])\).

Total New Old
Modular forms 204 20 184
Cusp forms 180 20 160
Eisenstein series 24 0 24

Trace form

\( 20 q - 24 q^{5} - 60 q^{9} + O(q^{10}) \) \( 20 q - 24 q^{5} - 60 q^{9} + 56 q^{13} + 24 q^{17} + 48 q^{21} + 28 q^{25} - 120 q^{29} - 104 q^{37} + 120 q^{41} + 72 q^{45} - 124 q^{49} + 168 q^{53} - 48 q^{57} - 8 q^{61} - 144 q^{65} + 8 q^{73} + 180 q^{81} - 48 q^{85} + 168 q^{89} - 144 q^{93} - 40 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(528, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
528.3.l.a 528.l 4.b $4$ $14.387$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 528.3.l.a \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-3-\beta _{2})q^{5}-6\beta _{1}q^{7}+\cdots\)
528.3.l.b 528.l 4.b $4$ $14.387$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 528.3.l.b \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-2q^{5}+(\beta _{1}+\beta _{3})q^{7}-3q^{9}+\cdots\)
528.3.l.c 528.l 4.b $4$ $14.387$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 528.3.l.c \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(3\beta _{1}+\beta _{3})q^{7}+\cdots\)
528.3.l.d 528.l 4.b $8$ $14.387$ 8.0.\(\cdots\).1 None 528.3.l.d \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-1-\beta _{5})q^{5}+(\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(528, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(528, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)