Space of modular forms of level 1035, weight 2, and Character 1035.b

• Label: 1035.2.b
• Level: $1035$
• Weight: $2$
• Character orbit: 1035.b
• Rep. character: $\chi_{1035}(829,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $7$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1035.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1035, [\chi])\).

	Total	New	Old
Modular forms	152	54	98
Cusp forms	136	54	82
Eisenstein series	16	0	16

Trace form

\( 54 q - 52 q^{4} - 2 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1035, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1035.2.b.a	$1035$	$2$	1035.b	5.b	$2$	$2$	$2$	$8.265$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-2q^{4}+(-2+i)q^{5}-iq^{7}+\cdots\)
1035.2.b.b	$1035$	$2$	1035.b	5.b	$2$	$2$	$2$	$8.265$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+(-2-i)q^{5}-2iq^{7}+\cdots\)
1035.2.b.c	$1035$	$2$	1035.b	5.b	$2$	$2$	$2$	$8.265$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+(-1+2i)q^{5}+3iq^{8}+\cdots\)
1035.2.b.d	$1035$	$2$	1035.b	5.b	$2$	$6$	$6$	$8.265$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(-1+\beta _{1}-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
1035.2.b.e	$1035$	$2$	1035.b	5.b	$2$	$8$	$8$	$8.265$	8.0.527896576.2	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}+(-1-\beta _{2}+\beta _{4}-\beta _{6})q^{4}+\cdots\)
1035.2.b.f	$1035$	$2$	1035.b	5.b	$2$	$14$	$14$	$8.265$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+(-2-\beta _{8}+\beta _{9})q^{4}-\beta _{10}q^{5}+\cdots\)
1035.2.b.g	$1035$	$2$	1035.b	5.b	$2$	$20$	$20$	$8.265$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{16}q^{2}+(-\beta _{2}-\beta _{5})q^{4}+\beta _{10}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1035, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1035, [\chi]) \cong \)