Space of modular forms of level 1040, weight 2, and Character 1040.q

• Label: 1040.2.q
• Level: $1040$
• Weight: $2$
• Character orbit: 1040.q
• Rep. character: $\chi_{1040}(81,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $56$
• Newform subspaces: $18$
• Sturm bound: $336$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(336\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1040, [\chi])\).

	Total	New	Old
Modular forms	360	56	304
Cusp forms	312	56	256
Eisenstein series	48	0	48

Trace form

\( 56 q - 4 q^{3} + 4 q^{7} - 28 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1040, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1040.2.q.a	$1040$	$2$	1040.q	13.c	$3$	$2$	$1$	$8.304$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-3\)	\(-2\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-3+3\zeta_{6})q^{3}-q^{5}+3\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots\)
1040.2.q.b	$1040$	$2$	1040.q	13.c	$3$	$2$	$1$	$8.304$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-3\)	\(2\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-3+3\zeta_{6})q^{3}+q^{5}+3\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots\)
1040.2.q.c	$1040$	$2$	1040.q	13.c	$3$	$2$	$1$	$8.304$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(-2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}-q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1040.2.q.d	$1040$	$2$	1040.q	13.c	$3$	$2$	$1$	$8.304$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-q^{5}-3\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1040.2.q.e	$1040$	$2$	1040.q	13.c	$3$	$2$	$1$	$8.304$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-q^{5}-3\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1040.2.q.f	$1040$	$2$	1040.q	13.c	$3$	$2$	$1$	$8.304$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-q^{5}+5\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1040.2.q.g	$1040$	$2$	1040.q	13.c	$3$	$2$	$1$	$8.304$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+q^{5}-3\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1040.2.q.h	$1040$	$2$	1040.q	13.c	$3$	$2$	$1$	$8.304$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{5}-3\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(-3+3\zeta_{6})q^{11}+\cdots\)
1040.2.q.i	$1040$	$2$	1040.q	13.c	$3$	$2$	$1$	$8.304$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(-2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-q^{5}-\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1040.2.q.j	$1040$	$2$	1040.q	13.c	$3$	$2$	$1$	$8.304$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+q^{5}-\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1040.2.q.k	$1040$	$2$	1040.q	13.c	$3$	$2$	$1$	$8.304$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(2\)	\(-2\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{3}-q^{5}+3\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1040.2.q.l	$1040$	$2$	1040.q	13.c	$3$	$4$	$2$	$8.304$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(-1\)	\(4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}+q^{5}+(1-\beta _{2})q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
1040.2.q.m	$1040$	$2$	1040.q	13.c	$3$	$4$	$2$	$8.304$	\(\Q(\sqrt{-3}, \sqrt{10})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}-q^{5}+\beta _{2}q^{7}+7\beta _{2}q^{9}+(-1+\cdots)q^{11}+\cdots\)
1040.2.q.n	$1040$	$2$	1040.q	13.c	$3$	$4$	$2$	$8.304$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{3}+q^{5}+(-2\beta _{1}+\beta _{2}+\beta _{3})q^{7}+\cdots\)
1040.2.q.o	$1040$	$2$	1040.q	13.c	$3$	$4$	$2$	$8.304$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(2\)	\(-4\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}-q^{5}+(-1+\beta _{1})q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
1040.2.q.p	$1040$	$2$	1040.q	13.c	$3$	$4$	$2$	$8.304$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(2\)	\(4\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+q^{5}+(-1+\zeta_{12}+\cdots)q^{7}+\cdots\)
1040.2.q.q	$1040$	$2$	1040.q	13.c	$3$	$6$	$3$	$8.304$	6.0.27870912.1	None		$2$	$0$	\(0\)	\(1\)	\(-6\)	\(9\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2})q^{3}-q^{5}+3\beta _{4}q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
1040.2.q.r	$1040$	$2$	1040.q	13.c	$3$	$8$	$4$	$8.304$	8.0.649638144.4	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(-4\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{3}+q^{5}+(-1-\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1040, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1040, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)