Space of modular forms of level 1155, weight 2, and Character 1155.l

• Label: 1155.2.l
• Level: $1155$
• Weight: $2$
• Character orbit: 1155.l
• Rep. character: $\chi_{1155}(1121,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $6$
• Sturm bound: $384$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(384\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1155, [\chi])\).

	Total	New	Old
Modular forms	200	96	104
Cusp forms	184	96	88
Eisenstein series	16	0	16

Trace form

\( 96 q + 8 q^{3} + 96 q^{4} - 20 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1155, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1155.2.l.a	$1155$	$2$	1155.l	33.d	$2$	$4$	$4$	$9.223$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(-4\)	\(4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}^{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
1155.2.l.b	$1155$	$2$	1155.l	33.d	$2$	$4$	$4$	$9.223$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(-2\zeta_{8}+\cdots)q^{6}+\cdots\)
1155.2.l.c	$1155$	$2$	1155.l	33.d	$2$	$4$	$4$	$9.223$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(-2\zeta_{8}+\cdots)q^{6}+\cdots\)
1155.2.l.d	$1155$	$2$	1155.l	33.d	$2$	$4$	$4$	$9.223$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(4\)	\(4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}^{2})q^{3}+(1-2\zeta_{8}^{3})q^{4}+\cdots\)
1155.2.l.e	$1155$	$2$	1155.l	33.d	$2$	$40$	$40$	$9.223$		None		$2$	$0$	\(-4\)	\(-4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1155.2.l.f	$1155$	$2$	1155.l	33.d	$2$	$40$	$40$	$9.223$		None		$2$	$0$	\(4\)	\(-4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1155, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1155, [\chi]) \cong \)