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Properties

Label 528.2.y
Level $528$
Weight $2$
Character orbit 528.y
Rep. character $\chi_{528}(49,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $48$
Newform subspaces $11$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 528.y (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 11 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(528, [\chi])\).

Total New Old
Modular forms 432 48 384
Cusp forms 336 48 288
Eisenstein series 96 0 96

Trace form

\( 48 q + 4 q^{7} - 12 q^{9} + O(q^{10}) \) \( 48 q + 4 q^{7} - 12 q^{9} + 4 q^{11} - 12 q^{19} - 16 q^{23} - 4 q^{25} - 16 q^{29} + 4 q^{33} + 36 q^{35} + 24 q^{37} + 8 q^{39} - 24 q^{41} + 72 q^{43} + 36 q^{47} - 28 q^{49} - 12 q^{51} + 40 q^{53} + 44 q^{55} - 8 q^{59} + 16 q^{61} + 4 q^{63} + 16 q^{65} - 16 q^{67} + 4 q^{71} - 12 q^{73} - 24 q^{75} - 40 q^{77} - 16 q^{79} - 12 q^{81} - 84 q^{83} - 24 q^{85} - 72 q^{87} - 16 q^{89} - 20 q^{91} - 24 q^{93} - 60 q^{95} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(528, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
528.2.y.a 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None \(0\) \(-1\) \(-7\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}+(-3+2\zeta_{10}-3\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
528.2.y.b 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None \(0\) \(-1\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}+(-1-\zeta_{10}^{2})q^{5}-\zeta_{10}^{3}q^{7}+\cdots\)
528.2.y.c 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None \(0\) \(-1\) \(3\) \(-5\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}+(1+\zeta_{10}^{2})q^{5}+(-2+2\zeta_{10}+\cdots)q^{7}+\cdots\)
528.2.y.d 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None \(0\) \(-1\) \(8\) \(6\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}+(3-\zeta_{10}+3\zeta_{10}^{2})q^{5}+\cdots\)
528.2.y.e 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None \(0\) \(1\) \(-8\) \(-6\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}+(-3+\zeta_{10}-3\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
528.2.y.f 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None \(0\) \(1\) \(-1\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}+(-1+2\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
528.2.y.g 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None \(0\) \(1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}+(1-3\zeta_{10}+\zeta_{10}^{2})q^{5}+\cdots\)
528.2.y.h 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None \(0\) \(1\) \(1\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}+(1-2\zeta_{10}+\zeta_{10}^{2})q^{5}+\cdots\)
528.2.y.i 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None \(0\) \(1\) \(3\) \(-7\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}+(1+\zeta_{10}^{2})q^{5}+(-2+2\zeta_{10}+\cdots)q^{7}+\cdots\)
528.2.y.j 528.y 11.c $4$ $4.216$ \(\Q(\zeta_{10})\) None \(0\) \(1\) \(5\) \(7\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}+(1+2\zeta_{10}+\zeta_{10}^{2})q^{5}+\cdots\)
528.2.y.k 528.y 11.c $8$ $4.216$ 8.0.185640625.1 None \(0\) \(-2\) \(-1\) \(5\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{6}q^{3}+(-2\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(528, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(528, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)