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

• Label: 1104.2.e
• Level: $1104$
• Weight: $2$
• Character orbit: 1104.e
• Rep. character: $\chi_{1104}(47,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $8$
• Sturm bound: $384$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1104 = 2^{4} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1104.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(384\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	204	44	160
Cusp forms	180	44	136
Eisenstein series	24	0	24

Trace form

\( 44 q + 12 q^{9} + O(q^{10}) \)

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.e.a	$1104$	$2$	1104.e	12.b	$2$	$2$	$2$	$8.815$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}+(3-3\zeta_{6})q^{9}+\cdots\)
1104.2.e.b	$1104$	$2$	1104.e	12.b	$2$	$2$	$2$	$8.815$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2-\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}+(3-3\zeta_{6})q^{9}+\cdots\)
1104.2.e.c	$1104$	$2$	1104.e	12.b	$2$	$4$	$4$	$8.815$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+2\beta _{2}q^{7}+(1-\beta _{2}-\beta _{3})q^{9}+\cdots\)
1104.2.e.d	$1104$	$2$	1104.e	12.b	$2$	$4$	$4$	$8.815$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+2\beta _{2}q^{7}+(1+\beta _{2}-\beta _{3})q^{9}+\cdots\)
1104.2.e.e	$1104$	$2$	1104.e	12.b	$2$	$8$	$8$	$8.815$	8.0.12960000.1	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{7})q^{3}+(\beta _{2}-\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1104.2.e.f	$1104$	$2$	1104.e	12.b	$2$	$8$	$8$	$8.815$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{3}-\beta _{1}q^{5}-\beta _{1}q^{7}+\beta _{2}q^{9}+\cdots\)
1104.2.e.g	$1104$	$2$	1104.e	12.b	$2$	$8$	$8$	$8.815$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{3}-\beta _{1}q^{5}+\beta _{1}q^{7}+\beta _{2}q^{9}+\cdots\)
1104.2.e.h	$1104$	$2$	1104.e	12.b	$2$	$8$	$8$	$8.815$	8.0.12960000.1	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{7})q^{3}+(\beta _{2}-\beta _{5})q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots\)

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

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