Properties

Label 1064.2.q
Level $1064$
Weight $2$
Character orbit 1064.q
Rep. character $\chi_{1064}(305,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $72$
Newform subspaces $15$
Sturm bound $320$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1064.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 15 \)
Sturm bound: \(320\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\)

Dimensions

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

Total New Old
Modular forms 336 72 264
Cusp forms 304 72 232
Eisenstein series 32 0 32

Trace form

\( 72 q - 4 q^{5} - 4 q^{7} - 32 q^{9} + O(q^{10}) \) \( 72 q - 4 q^{5} - 4 q^{7} - 32 q^{9} - 8 q^{15} - 8 q^{17} + 6 q^{19} + 12 q^{21} - 6 q^{23} - 48 q^{25} - 24 q^{27} + 24 q^{29} + 4 q^{31} - 4 q^{33} + 12 q^{35} + 30 q^{39} - 8 q^{41} + 16 q^{43} - 24 q^{45} + 6 q^{47} + 28 q^{51} - 8 q^{53} - 4 q^{55} + 10 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} - 80 q^{71} + 16 q^{73} - 8 q^{75} - 26 q^{77} + 16 q^{79} - 44 q^{81} - 76 q^{83} + 44 q^{85} - 28 q^{87} - 4 q^{89} - 40 q^{93} + 24 q^{99} + O(q^{100}) \)

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.q.a 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1064.2.q.b 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1064.2.q.c 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1064.2.q.d 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-3\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
1064.2.q.e 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-3\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+(-5+\cdots)q^{11}+\cdots\)
1064.2.q.f 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
1064.2.q.g 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+3\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots\)
1064.2.q.h 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
1064.2.q.i 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)
1064.2.q.j 1064.q 7.c $2$ $8.496$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1064.2.q.k 1064.q 7.c $4$ $8.496$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-4\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2})q^{5}+\cdots\)
1064.2.q.l 1064.q 7.c $4$ $8.496$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(4\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{2}q^{3}+(1-\beta _{2})q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\cdots\)
1064.2.q.m 1064.q 7.c $6$ $8.496$ 6.0.31259952.1 None \(0\) \(0\) \(-2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{5})q^{5}+\cdots\)
1064.2.q.n 1064.q 7.c $16$ $8.496$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+\beta _{10}q^{5}+\beta _{11}q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots\)
1064.2.q.o 1064.q 7.c $22$ $8.496$ None \(0\) \(0\) \(-3\) \(-6\) $\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(1064, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(532, [\chi])\)\(^{\oplus 2}\)