Space of modular forms of level 1148, weight 2, and Character 1148.i

• Label: 1148.2.i
• Level: $1148$
• Weight: $2$
• Character orbit: 1148.i
• Rep. character: $\chi_{1148}(165,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $52$
• Newform subspaces: $5$
• Sturm bound: $336$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(336\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1148, [\chi])\).

	Total	New	Old
Modular forms	348	52	296
Cusp forms	324	52	272
Eisenstein series	24	0	24

Trace form

\( 52 q + 2 q^{3} + 2 q^{5} + 8 q^{7} - 28 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1148, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1148.2.i.a	$1148$	$2$	1148.i	7.c	$3$	$2$	$1$	$9.167$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(3\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1148.2.i.b	$1148$	$2$	1148.i	7.c	$3$	$2$	$1$	$9.167$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
1148.2.i.c	$1148$	$2$	1148.i	7.c	$3$	$2$	$1$	$9.167$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1148.2.i.d	$1148$	$2$	1148.i	7.c	$3$	$16$	$8$	$9.167$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}+\beta _{14}q^{5}+(-\beta _{5}+\beta _{8})q^{7}+\cdots\)
1148.2.i.e	$1148$	$2$	1148.i	7.c	$3$	$30$	$15$	$9.167$		None		$2$	$0$	\(0\)	\(1\)	\(-3\)	\(3\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1148, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1148, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(574, [\chi])\)\(^{\oplus 2}\)