Space of modular forms of level 1104, weight 5, and Character 1104.c

• Label: 1104.5.c
• Level: $1104$
• Weight: $5$
• Character orbit: 1104.c
• Rep. character: $\chi_{1104}(1057,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $4$
• Sturm bound: $960$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 1104 = 2^{4} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	1104.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(960\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(1104, [\chi])\).

	Total	New	Old
Modular forms	780	96	684
Cusp forms	756	96	660
Eisenstein series	24	0	24

Trace form

\( 96 q + 2592 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(1104, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1104.5.c.a	$1104$	$5$	1104.c	23.b	$2$	$16$	$16$	$114.120$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}\cdot 3^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{3}q^{5}+(-\beta _{2}+\beta _{9})q^{7}+\cdots\)
1104.5.c.b	$1104$	$5$	1104.c	23.b	$2$	$16$	$16$	$114.120$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+\beta _{1}q^{5}-\beta _{7}q^{7}+3^{3}q^{9}+\cdots\)
1104.5.c.c	$1104$	$5$	1104.c	23.b	$2$	$16$	$16$	$114.120$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}\cdot 3^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{10}q^{5}+\beta _{11}q^{7}+3^{3}q^{9}+\cdots\)
1104.5.c.d	$1104$	$5$	1104.c	23.b	$2$	$48$	$48$	$114.120$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{5}^{\mathrm{old}}(1104, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(1104, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(368, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(552, [\chi])\)\(^{\oplus 2}\)