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

• Label: 1040.2.k
• Level: $1040$
• Weight: $2$
• Character orbit: 1040.k
• Rep. character: $\chi_{1040}(961,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $5$
• Sturm bound: $336$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(336\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	180	28	152
Cusp forms	156	28	128
Eisenstein series	24	0	24

Trace form

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

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.k.a	$1040$	$2$	1040.k	13.b	$2$	$2$	$2$	$8.304$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{3}-iq^{5}+q^{9}+(2+3i)q^{13}+\cdots\)
1040.2.k.b	$1040$	$2$	1040.k	13.b	$2$	$6$	$6$	$8.304$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots\)
1040.2.k.c	$1040$	$2$	1040.k	13.b	$2$	$6$	$6$	$8.304$	6.0.9144576.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}-\beta _{2}q^{5}+(\beta _{1}+\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots\)
1040.2.k.d	$1040$	$2$	1040.k	13.b	$2$	$6$	$6$	$8.304$	6.0.5089536.1	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{1})q^{3}+\beta _{4}q^{5}+(-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
1040.2.k.e	$1040$	$2$	1040.k	13.b	$2$	$8$	$8$	$8.304$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1040, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)