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

• Label: 1035.2.c
• Level: $1035$
• Weight: $2$
• Character orbit: 1035.c
• Rep. character: $\chi_{1035}(206,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $4$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1035.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	152	32	120
Cusp forms	136	32	104
Eisenstein series	16	0	16

Trace form

\( 32 q - 40 q^{4} + O(q^{10}) \)

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.c.a	$1035$	$2$	1035.c	69.c	$2$	$4$	$4$	$8.265$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{5}+(\beta _{1}+\beta _{2})q^{7}-2\beta _{2}q^{8}+\cdots\)
1035.2.c.b	$1035$	$2$	1035.c	69.c	$2$	$4$	$4$	$8.265$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+q^{5}+\beta _{1}q^{7}-2\beta _{2}q^{8}-\beta _{2}q^{10}+\cdots\)
1035.2.c.c	$1035$	$2$	1035.c	69.c	$2$	$12$	$12$	$8.265$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-q^{5}+\beta _{9}q^{7}+\cdots\)
1035.2.c.d	$1035$	$2$	1035.c	69.c	$2$	$12$	$12$	$8.265$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+q^{5}-\beta _{9}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1035, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)