Space of modular forms of level 1045, weight 2, and Character 1045.b

• Label: 1045.2.b
• Level: $1045$
• Weight: $2$
• Character orbit: 1045.b
• Rep. character: $\chi_{1045}(419,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $5$
• Sturm bound: $240$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(240\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1045, [\chi])\).

	Total	New	Old
Modular forms	124	92	32
Cusp forms	116	92	24
Eisenstein series	8	0	8

Trace form

\( 92 q - 96 q^{4} + 6 q^{5} - 8 q^{6} - 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1045, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1045.2.b.a	$1045$	$2$	1045.b	5.b	$2$	$4$	$4$	$8.344$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots\)
1045.2.b.b	$1045$	$2$	1045.b	5.b	$2$	$16$	$16$	$8.344$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{11}q^{3}+\beta _{2}q^{4}+(\beta _{3}+\beta _{13}+\cdots)q^{5}+\cdots\)
1045.2.b.c	$1045$	$2$	1045.b	5.b	$2$	$20$	$20$	$8.344$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2})q^{4}-\beta _{11}q^{5}+\cdots\)
1045.2.b.d	$1045$	$2$	1045.b	5.b	$2$	$22$	$22$	$8.344$		None		$2$	$0$	\(0\)	\(0\)	\(7\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1045.2.b.e	$1045$	$2$	1045.b	5.b	$2$	$30$	$30$	$8.344$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1045, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)