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Properties

Label 1064.2.a
Level $1064$
Weight $2$
Character orbit 1064.a
Rep. character $\chi_{1064}(1,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $9$
Sturm bound $320$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1064.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(320\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1064))\).

Total New Old
Modular forms 168 26 142
Cusp forms 153 26 127
Eisenstein series 15 0 15

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

\(2\)\(7\)\(19\)FrickeDim
\(+\)\(+\)\(+\)$+$\(2\)
\(+\)\(+\)\(-\)$-$\(5\)
\(+\)\(-\)\(+\)$-$\(5\)
\(+\)\(-\)\(-\)$+$\(2\)
\(-\)\(+\)\(+\)$-$\(4\)
\(-\)\(+\)\(-\)$+$\(2\)
\(-\)\(-\)\(+\)$+$\(2\)
\(-\)\(-\)\(-\)$-$\(4\)
Plus space\(+\)\(8\)
Minus space\(-\)\(18\)

Trace form

\( 26 q + 4 q^{5} + 22 q^{9} + O(q^{10}) \) \( 26 q + 4 q^{5} + 22 q^{9} + 12 q^{11} - 4 q^{13} + 24 q^{15} + 4 q^{17} + 18 q^{25} + 24 q^{27} - 4 q^{29} - 16 q^{31} + 12 q^{35} + 28 q^{37} + 8 q^{39} - 4 q^{41} + 4 q^{43} + 44 q^{45} + 48 q^{47} + 26 q^{49} + 16 q^{51} + 28 q^{53} - 16 q^{55} - 4 q^{57} + 16 q^{59} + 12 q^{61} + 8 q^{65} - 16 q^{67} + 24 q^{69} + 24 q^{71} - 12 q^{73} - 16 q^{75} - 8 q^{77} + 8 q^{79} - 6 q^{81} - 48 q^{83} - 8 q^{85} - 20 q^{89} - 8 q^{91} - 8 q^{93} - 44 q^{97} + 20 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1064))\) 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 7 19
1064.2.a.a 1064.a 1.a $2$ $8.496$ \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(1-2\beta )q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots\)
1064.2.a.b 1064.a 1.a $2$ $8.496$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}-q^{7}+\beta q^{9}+(-1+\beta )q^{11}+\cdots\)
1064.2.a.c 1064.a 1.a $2$ $8.496$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1+2\beta )q^{5}+q^{7}+(-2+\cdots)q^{9}+\cdots\)
1064.2.a.d 1064.a 1.a $2$ $8.496$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(-2\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}-q^{7}+(-2+\beta )q^{9}+(1+\cdots)q^{11}+\cdots\)
1064.2.a.e 1064.a 1.a $2$ $8.496$ \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(5\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(2+\beta )q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots\)
1064.2.a.f 1064.a 1.a $3$ $8.496$ 3.3.1101.1 None \(0\) \(-1\) \(2\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+q^{7}+(4-\beta _{1}+\cdots)q^{9}+\cdots\)
1064.2.a.g 1064.a 1.a $4$ $8.496$ 4.4.18097.1 None \(0\) \(0\) \(-3\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+(-1-\beta _{2}+\beta _{3})q^{5}-q^{7}+\cdots\)
1064.2.a.h 1064.a 1.a $4$ $8.496$ 4.4.25857.1 None \(0\) \(2\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+q^{7}+\cdots\)
1064.2.a.i 1064.a 1.a $5$ $8.496$ 5.5.10463409.1 None \(0\) \(0\) \(3\) \(-5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1-\beta _{4})q^{5}-q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1064))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1064)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(532))\)\(^{\oplus 2}\)