Space of modular forms of level 1104, weight 2, and Character 1104.i

• Label: 1104.2.i
• Level: $1104$
• Weight: $2$
• Character orbit: 1104.i
• Rep. character: $\chi_{1104}(367,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1104 = 2^{4} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1104.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 92 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1104, [\chi])\).

	Total	New	Old
Modular forms	204	24	180
Cusp forms	180	24	156
Eisenstein series	24	0	24

Trace form

\( 24 q - 24 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1104, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1104.2.i.a	$1104$	$2$	1104.i	92.b	$2$	$8$	$8$	$8.815$	8.0.\(\cdots\).8	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{3}q^{5}-\beta _{4}q^{7}-q^{9}-2\beta _{1}q^{11}+\cdots\)
1104.2.i.b	$1104$	$2$	1104.i	92.b	$2$	$16$	$16$	$8.815$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}-\beta _{14}q^{5}+\beta _{12}q^{7}-q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1104, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1104, [\chi]) \cong \)