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

• Label: 1148.2.n
• Level: $1148$
• Weight: $2$
• Character orbit: 1148.n
• Rep. character: $\chi_{1148}(57,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $80$
• Newform subspaces: $5$
• Sturm bound: $336$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.n (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(336\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	696	80	616
Cusp forms	648	80	568
Eisenstein series	48	0	48

Trace form

\( 80 q + 4 q^{3} + 4 q^{5} + 68 q^{9} + O(q^{10}) \)

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.n.a	$1148$	$2$	1148.n	41.d	$5$	$8$	$2$	$9.167$	8.0.64000000.2	None		$2$	$0$	\(0\)	\(-4\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{3}+\beta _{4}+\beta _{6}-\beta _{7})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1148.2.n.b	$1148$	$2$	1148.n	41.d	$5$	$8$	$2$	$9.167$	8.0.64000000.2	None		$2$	$0$	\(0\)	\(8\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1+\beta _{5})q^{3}+(\beta _{2}+\beta _{7})q^{5}+\beta _{4}q^{7}+\cdots\)
1148.2.n.c	$1148$	$2$	1148.n	41.d	$5$	$16$	$4$	$9.167$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(-13\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{1}-\beta _{2}+\beta _{5}-\beta _{6})q^{3}+(-1+\cdots)q^{5}+\cdots\)
1148.2.n.d	$1148$	$2$	1148.n	41.d	$5$	$24$	$6$	$9.167$		None		$2$	$0$	\(0\)	\(-10\)	\(4\)	\(-6\)		$\mathrm{SU}(2)[C_{5}]$
1148.2.n.e	$1148$	$2$	1148.n	41.d	$5$	$24$	$6$	$9.167$		None		$2$	$0$	\(0\)	\(12\)	\(17\)	\(6\)		$\mathrm{SU}(2)[C_{5}]$

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

\( S_{2}^{\mathrm{old}}(1148, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 2}\)