Properties

Label 1064.2.s
Level $1064$
Weight $2$
Character orbit 1064.s
Rep. character $\chi_{1064}(121,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $5$
Sturm bound $320$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1064.s (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(320\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1064, [\chi])\).

Total New Old
Modular forms 336 80 256
Cusp forms 304 80 224
Eisenstein series 32 0 32

Trace form

\( 80 q - 4 q^{3} + 2 q^{7} - 40 q^{9} + O(q^{10}) \) \( 80 q - 4 q^{3} + 2 q^{7} - 40 q^{9} + 2 q^{11} + 2 q^{13} - 4 q^{15} + 2 q^{17} + 6 q^{19} + 2 q^{21} + 2 q^{23} + 88 q^{25} + 32 q^{27} + 2 q^{29} - 8 q^{31} - 16 q^{33} - 6 q^{35} - 14 q^{37} - 12 q^{39} + 10 q^{41} - 4 q^{43} + 8 q^{45} - 6 q^{47} + 2 q^{49} + 12 q^{53} + 6 q^{55} - 2 q^{57} - 24 q^{59} - 2 q^{61} + 8 q^{63} + 24 q^{65} + 4 q^{67} - 40 q^{69} + 8 q^{71} - 18 q^{73} - 46 q^{75} - 10 q^{77} + 36 q^{79} - 64 q^{81} + 4 q^{83} + 34 q^{85} + 12 q^{87} + 36 q^{89} - 26 q^{91} + 28 q^{93} + 30 q^{95} + 4 q^{97} + 42 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1064, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1064.2.s.a 1064.s 133.h $2$ $8.496$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{3}+2q^{5}+(3-2\zeta_{6})q^{7}+(2-2\zeta_{6})q^{9}+\cdots\)
1064.2.s.b 1064.s 133.h $2$ $8.496$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{3}+2q^{5}+(1+2\zeta_{6})q^{7}+(2-2\zeta_{6})q^{9}+\cdots\)
1064.2.s.c 1064.s 133.h $4$ $8.496$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(0\) \(1\) \(-6\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(-3+2\beta _{2}+\cdots)q^{7}+\cdots\)
1064.2.s.d 1064.s 133.h $32$ $8.496$ None \(0\) \(-3\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$
1064.2.s.e 1064.s 133.h $40$ $8.496$ None \(0\) \(-2\) \(-4\) \(1\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1064, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1064, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(532, [\chi])\)\(^{\oplus 2}\)