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

• Label: 1155.2.c
• Level: $1155$
• Weight: $2$
• Character orbit: 1155.c
• Rep. character: $\chi_{1155}(694,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $6$
• Sturm bound: $384$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(384\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(2\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	200	56	144
Cusp forms	184	56	128
Eisenstein series	16	0	16

Trace form

\( 56 q - 56 q^{4} - 8 q^{5} + 8 q^{6} - 56 q^{9} + O(q^{10}) \)

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.c.a	$1155$	$2$	1155.c	5.b	$2$	$2$	$2$	$9.223$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}+q^{4}+(-2+i)q^{5}+\cdots\)
1155.2.c.b	$1155$	$2$	1155.c	5.b	$2$	$2$	$2$	$9.223$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}+q^{4}+(-2-i)q^{5}+\cdots\)
1155.2.c.c	$1155$	$2$	1155.c	5.b	$2$	$6$	$6$	$9.223$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
1155.2.c.d	$1155$	$2$	1155.c	5.b	$2$	$6$	$6$	$9.223$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
1155.2.c.e	$1155$	$2$	1155.c	5.b	$2$	$20$	$20$	$9.223$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{13}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
1155.2.c.f	$1155$	$2$	1155.c	5.b	$2$	$20$	$20$	$9.223$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{11}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)

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

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