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

• Label: 1155.2.i
• Level: $1155$
• Weight: $2$
• Character orbit: 1155.i
• Rep. character: $\chi_{1155}(76,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $4$
• Sturm bound: $384$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(384\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	200	64	136
Cusp forms	184	64	120
Eisenstein series	16	0	16

Trace form

\( 64 q - 72 q^{4} - 64 q^{9} + O(q^{10}) \)

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.i.a	$1155$	$2$	1155.i	77.b	$2$	$8$	$8$	$9.223$	8.0.303595776.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{5})q^{2}+\beta _{4}q^{3}+(-2-\beta _{7})q^{4}+\cdots\)
1155.2.i.b	$1155$	$2$	1155.i	77.b	$2$	$8$	$8$	$9.223$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{24}^{4}-\zeta_{24}^{5})q^{2}-\zeta_{24}^{3}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
1155.2.i.c	$1155$	$2$	1155.i	77.b	$2$	$16$	$16$	$9.223$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{2}+\beta _{9}q^{3}+(-2-\beta _{3})q^{4}-\beta _{9}q^{5}+\cdots\)
1155.2.i.d	$1155$	$2$	1155.i	77.b	$2$	$32$	$32$	$9.223$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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