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

• Label: 1104.2.m
• Level: $1104$
• Weight: $2$
• Character orbit: 1104.m
• Rep. character: $\chi_{1104}(689,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $5$
• Sturm bound: $384$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 1104 = 2^{4} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1104.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(384\)
Trace bound:			\(25\)
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	50	154
Cusp forms	180	46	134
Eisenstein series	24	4	20

Trace form

\( 46 q + 2 q^{3} - 2 q^{9} + O(q^{10}) \)

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.m.a	$1104$	$2$	1104.m	69.c	$2$	$6$	$6$	$8.815$	6.0.8869743.1	\(\Q(\sqrt{-23}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{3}-\beta _{3}q^{9}+(-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{13}+\cdots\)
1104.2.m.b	$1104$	$2$	1104.m	69.c	$2$	$8$	$8$	$8.815$	8.0.\(\cdots\).7	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}-\beta _{5}q^{5}-\beta _{7}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)
1104.2.m.c	$1104$	$2$	1104.m	69.c	$2$	$8$	$8$	$8.815$	8.0.40960000.1	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{4})q^{3}-\beta _{3}q^{5}-\beta _{5}q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
1104.2.m.d	$1104$	$2$	1104.m	69.c	$2$	$8$	$8$	$8.815$	8.0.\(\cdots\).3	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{4})q^{3}+\beta _{3}q^{5}-\beta _{5}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1104.2.m.e	$1104$	$2$	1104.m	69.c	$2$	$16$	$16$	$8.815$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{3}+\beta _{5}q^{5}-\beta _{1}q^{7}+(\beta _{2}+\beta _{4}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1104, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(552, [\chi])\)\(^{\oplus 2}\)